polynomials, expressions, and formulas or, how i learned to stop worrying and love the variable

Polynomials, Expressions, and FormulasOr, How I Learned to Stop Worrying and Love the Variable

OverviewWe begin this module with a study of numbers and the basic operations of addition, subtraction, multiplication, and division. The algebraic properties of these operations are introduced along with the conventions for the order in which the operations are performed in mathematical expressions. Lessons are included on numerical and variable expressions, as well as on writing, evaluating, and simplifying these expressions. These concepts are extended to polynomials, with lessons on simplifying, adding, subtracting, multiplying, dividing, and factoring polynomials. There are also lessons on more general formulas, including evaluating and rewriting formulas.

On the following Topics slide there is a link to a table of contents for each topic. Clicking on a link on a Contents slide will take you to the first lesson slide for that topic. In many cases, there will be more than one slide on that topic. Work through as many as you need to master the topic, and then go on to the next topic. Clicking on the heading for a slide will take you back to the Contents slide for that topic; clicking on Return to Topics List on the Contents slide will take you back to the main Topics page.

Topics• Sets of Real Numbers• Properties of Operations• Order of Operations• Numerical Expressions• Variables and Expressions• Writing Variable Expressions• Evaluating Variable Expressions• Simplifying Variable Expressions• Polynomial Expressions• Polynomial Multiplication• Polynomial Division• Factoring Polynomials• Formulas & Polynomials in Two (or more) Variables• Polynomial Functions

Sets of Real Numbers• Description and examples of subsets of the set of real

numbers, including the rational numbers and irrational numbers

• Subsets of the Real Numbers• Recognizing Irrational and Rational Numbers• Interactive Practice Problems: Recognizing Rational and Irratio

nal NumbersReturn to Topics List

CONTENTS:

Link: Number Sets

• Khan Academy video giving definitions of the various subsets of the real numbers

• Subsets include natural numbers, whole numbers, integers, rational numbers, and irrational numbers, with examples of numbers in each subset

• Time 5:17

Sets of Real Numbers

https://www.khanacademy.org/math/arithmetic/fractions/number_sets/v/number-sets

Link: Real Numbers

• Mathispower4u video on sets of real numbers• Describes various sets of real numbers, size comparison of real

numbers, and absolute values• Time 9:07


http://youtu.be/py-iSJziA_8

Link: Recognizing Irrational Numbers

• Khan Academy video explaining the difference between rational and irrational numbers

• Time 2:18


https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-irrational-numbers/v/recognizing-irrational-numbers

Link: Recognizing Rational and Irrational Numbers

• Khan Academy interactive practice problems on recognizing rational and irrational numbers

• A sequence of five practice problems is provided, along with• help with correct formats to enter answers• hints to help solve the problem, if needed• links to video lessons if you get stuck


https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-irrational-numbers/e/recognizing-rational-and-irrational-numbers

Properties of Operations• Descriptions and examples of properties of operations on numbers,

including commutative, associative, and distributive laws; identities and inverses for multiplication and addition

• Terminology of Properties of Numbers • Commutative Property of Addition• Commutative Property of Multiplication• Associative Law of Addition• Associative Law of Multiplication• Identity Properties of 0 and 1• Inverse Properties of Addition and Multiplication• The Distributive Property • Interactive Practice Problems: Distributive PropertyReturn to Topics List

CONTENTS:

Link: Properties of Numbers 1

• Khan Academy video examples recognizing the associative and commutative properties of arithmetic

• Time 2:03

Properties of Operations

https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/properties-of-numbers-1

Link: Number Properties Terminology 1

• Khan Academy video examples recognizing the distributive, associative, and commutative properties of arithmetic

• Time 3:05


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/number-properties-terminology-1

Link: Properties of Numbers 2

• Khan Academy video examples recognizing the properties of arithmetic

• Time 1:52


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/properties-of-numbers-2

Link: Commutative Law of Addition

• Khan Academy video example applying the commutative and associative laws of addition to rewrite a number expression

• Time 1:40


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/commutative-law-of-addition

Link: Commutative Property for Addition

• Khan Academy video example applying the commutative and associative laws of addition to rewrite a number expression

• Time 3:23


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/commutative-property-for-addition

Link: Commutative Property of Multiplication

• Khan Academy video example applying the commutative law of multiplication to rewrite a number expression

• Time 1:48


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/commutative-law-of-multiplication

Link: Associative Law of Addition

• Khan Academy video example applying the associative law of addition to rewrite a number expression

• Time 2:10


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/associative-law-of-addition

Link: Associative Law of Multiplication

• Khan Academy video example applying the associative law of multiplication to rewrite a number expression

• Time 2:15


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/associative-law-of-multiplication

Link: Identity Property of 0

• Khan Academy video examples demonstrating the additive identity property of 0

• Uses the method of the number line and absolute values when adding a zero in a numerical expression with more than one operation

• Time 4:46


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/identity-property-of-0

Link: Identity Property of 1

• Khan Academy video examples demonstrating the multiplicative identity property of 1, explaining that you always get the original term number as the answer

• Time 1:24


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/identity-property-of-1

Link: Identity Property of 1 (Second Example)

• Khan Academy video with more examples demonstrating the multiplicative identity property of 1

• Time 1:55


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/identity-property-of-1--second-example

Link: Inverse Property of Addition

• Khan Academy video examples of using the additive inverse to move from a given number back to zero

• The number line method is used to visualize the impact of adding the opposite of the given number

• Time 2:59


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/inverse-property-of-addition

Link: Inverse Property of Multiplication

• Khan Academy video examples demonstrating the multiplicative inverse property

• Uses the operation of division and builds to multiplication by the reciprocal

• Time 3:16


https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/inverse-property-of-multiplication

Link: The Distributive Property

• Khan Academy video example demonstrating the distributive property of multiplication over addition, with an explanation of why the distributive property works

• Time 4:56


https://www.khanacademy.org/math/arithmetic/order-of-operations/ditributive_property/v/the-distributive-property

Link: The Distributive Property 2

• Khan Academy video example demonstrating the distributive property of multiplication over subtraction

• Time 2:11


https://www.khanacademy.org/math/arithmetic/order-of-operations/ditributive_property/v/the-distributive-property-2

Link: The Distributive Property Example 1

• Khan Academy video examples demonstrating the distributive property in several algebraic expressions

• Examples require combining like terms and distributing fractions

• Time 5:39


https://www.khanacademy.org/math/arithmetic/order-of-operations/ditributive_property/v/distributive-property-example-1

Link: Distributive Property Exercise

• Khan Academy video examples demonstrating the distributive property of multiplication over addition in numerical expressions

• One problem reviews factoring the greatest common divisor and writing a distributive expression

• Time 3:03


https://www.khanacademy.org/math/arithmetic/order-of-operations/ditributive_property/v/distributive-property-exercise

Link: The Distributive Property

• Math Planet text and video examples demonstrating the distributive property in several situations

• Time 1:41


http://www.mathplanet.com/education/algebra-1/exploring-real-numbers/the-distributive-property

Link: Distributive Property

• Khan Academy interactive practice problems on the distributive property



https://www.khanacademy.org/math/arithmetic/order-of-operations/ditributive_property/e/distributive_property

Order of Operations• Descriptions and examples of the conventions on the order of

operations in numerical and variable expressions• Introduction to Order of Operations• Order of Operations Examples• Order of Operations With and Without Parentheses• Interactive Practice Problems: Order of Operations• Interactive Practice Problems: Expressions With ParenthesesReturn to Topics List

CONTENTS:

Link: Introduction to Order of Operations

• Khan Academy video introducing the order of operations on numbers

• Examples show the impact of the agreed upon order for simplifying numerical expressions

• Examples also explain operations at the same level and the “left to right” rule

• Time 9:40

Order of Operations

https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/v/introduction-to-order-of-operations

Link: The Order of Operations

• Mathispower4u video introducing the order of operations on numbers

• Includes several examples applying the order of operations to simplify expressions

• Time 6:31

Order of Operations

http://www.youtube.com/watch?v=WHTBgwBWlF4&feature=youtu.be

Link: Order of Operations

• Khan Academy video example applying the order of operations on numbers to simplify a numerical expression

• Time 4:27

Order of Operations

https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-order-of-operations/v/order-of-operations

Link: Order of Operations with Exponents

• Khan Academy video example applying the order of operations on numbers

• Time 4:36

Order of Operations

https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/v/order-of-operations-1

Link: More Complicated Order of Operations Example

• Khan Academy video advanced example applying the order of operations to a numerical expression involving parentheses

• Time 5:20

Order of Operations

https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/v/more-complicated-order-of-operations-example

Link: Order of Operations Examples

• Khan Academy video advanced examples applying the order of operations on numbers

• Time 14:23

Order of Operations

https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/v/order-of-operations-example

Link: Evaluating an Expression With and Without Parentheses

• Khan Academy video example demonstrating the effect of parentheses on the order of operations of numbers

• Time 2:06

Order of Operations

https://www.khanacademy.org/math/arithmetic/applying-math-reasoning-topic/constructing-numeric-expressions/v/evaluating-an-expression-with-and-without-parentheses

Link: Order of Operations

• Khan Academy interactive practice problems on order of operations of numbers


Order of Operations

https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/e/order_of_operations_2

Link: Order of Operations with Negative Numbers

• Khan Academy interactive practice problems on order of operations of numbers


Order of Operations

https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-variables-expressions/cc-7th-order-of-operations/e/order_of_operations

Link: Expressions With Parentheses

• Khan Academy interactive practice problems on evaluating numerical expressions containing parentheses


Order of Operations

https://www.khanacademy.org/math/arithmetic/applying-math-reasoning-topic/constructing-numeric-expressions/e/expressions-with-parentheses

Numerical Expressions• Examples and interactive problems on writing numerical

expressions from verbal phrases• Constructing Numerical Expressions Example• Interactive Practice Problems: Writing Numerical ExpressionsReturn to Topics List

CONTENTS:

Link: Constructing Numerical Expressions Example

• Khan Academy Video example constructing a numerical expression from a verbal phrase

• Time 1:22

Numerical Expressions

https://www.khanacademy.org/math/arithmetic/applying-math-reasoning-topic/constructing-numeric-expressions/v/constructing-numerical-expressions-example

Link: Writing Numerical Expressions with Exponents

• Khan Academy interactive practice problems on writing numerical expressions from verbal phrases



https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-writing-expressions/e/writing-expressions-3

Link: Writing Numerical Expressions with Exponents Word Problems

• Khan Academy interactive practice problems on writing numerical expressions with exponents from word problems



https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-writing-expressions/e/writing-numerical-expressions-with-exponents-word-problems

Variables and Expressions• Description and examples of variables and expressions• What is a Variable?• Introduction to Variables and Expressions• Notations for Multiplication With VariablesReturn to Topics List

CONTENTS:

Link: What is a Variable?

• Khan Academy video example introducing the concept of a variable

• Time 3:18

Variables and Expressions

https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/what-is-a-variable

Link: Introduction to Variables and Variable Expressions

• Mathispower4u video introducing and explaining the concepts of variables and variable expressions

• Also explains the difference between an expression and an equation

• Includes examples of • writing variable expressions from verbal phrases• evaluating a variable expression at a number

• Time 7:55


http://www.youtube.com/watch?v=fdzrf_EZrM8

Link: Why Aren't We Using the Multiplication Sign?

• Khan Academy video examples demonstrating the use of variables and various notation for multiplication with variables

• Time 4:58


https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/why-aren-t-we-using-the-multiplication-sign

Writing Variable Expressions• Translating verbal phrases into mathematical expressions• Constructing Algebraic Expressions from Verbal Phrases• Writing an Equation from a Word Problem• Interactive Practice Problems: Writing Simple Variable Expressi

ons• Interactive Practice Problems: Writing Compound Variable Exp

ressions• Interactive Practice Problems: Writing Expressions from Word

Problems Return to Topics List

CONTENTS:

Link: How Do You Turn a Simple Verbal Phrase Into an Algebraic Expression?

• Virtual Nerd video introduction to translating verbal phrases into algebraic expressions

• Examples are given of very basic phrases that require each of the operations of addition, subtraction, multiplication, and division

• Translates words such as sum, total, difference, product, quotient, and ratio

• Time 3:36

Writing Variable Expressions

http://www.virtualnerd.com/algebra-1/algebra-foundations/variables-expressions/words-to-math-translation/single-variable-phrase-translation-to-math

Link: How Do You Turn a Longer Verbal Phrase Into an Algebraic Expression?

• Virtual Nerd video example of translating a verbal phrase into an equation

• The example given is a compound phrase involving addition, multiplication, and fractions

• This example is also used in the video How Do You Write an Equation from a Word Problem?

• Time 5:10


http://www.virtualnerd.com/algebra-1/algebra-foundations/variables-expressions/words-to-math-translation/translating-words-to-math

http://www.virtualnerd.com/algebra-1/algebra-foundations/variables-expressions/words-to-math-translation/word-problem-equation-writing

Link: Ex 1: Writing Basic Algebraic Expressions

• Mathispower4u video introduction to translating verbal phrases into algebraic expressions

• Examples are given of very basic phrases that require each of the operations of addition and subtraction

• Time 1:59


http://youtu.be/SRRgpq4a-zU

Link: Ex 2: Writing Basic Algebraic Expressions

• Mathispower4u video example of translating a verbal phrase into an algebraic expression

• Example expresses the remaining part of a total distance in terms of the total and a given part of the total

• Time 2:35


http://youtu.be/-b1pKedxCeo

Link: Writing Expressions 1

• Khan Academy video examples writing variable expressions from verbal phrases

• Vocabulary reviewed in the examples includes quantity, sum, and product translated into mathematical expressions

• Time 1:38


https://www.khanacademy.org/math/algebra/introduction-to-algebra/writing-expressions-tutorial/v/writing-expressions-1


• Khan Academy video examples writing variable expressions from verbal phrases

• Time 2:45


https://www.khanacademy.org/math/algebra/introduction-to-algebra/writing-expressions-tutorial/v/writing-expressions-2

Link: Writing Expressions 2 Exercise Example

• Khan Academy video multiple choice example writing a variable expression from a verbal phrase

• Explains why some selections are incorrect and one is correct• Time 2:23


https://www.khanacademy.org/math/algebra/introduction-to-algebra/writing-expressions-tutorial/v/writing-expressions-2-exercise-example

Link: Writing Expressions 3 Exercise Example 1

• Khan Academy video example writing an expression in two variables from a complex word problem

• Time 2:24


https://www.khanacademy.org/math/algebra/introduction-to-algebra/writing-expressions-tutorial/v/writing-expressions-3-exercise-example-1


• Khan Academy video example writing an expression in one variable from a verbal phrase

• Example involves a word problem about volumes of cubes• Time 1:20




• Khan Academy video example writing an expression in several variables from a verbal phrase

• Time 0:43



Link: How Do You Write an Equation from a Word Problem?

• Virtual Nerd video example of translating the phrases in a “word problem” into variables and an equation

• See also the video How Do You Turn a Longer Verbal Phrase Into an Algebraic Expression?

• Time 4:00


http://www.virtualnerd.com/algebra-1/algebra-foundations/variables-expressions/words-to-math-translation/word-problem-equation-writing



Link: Connect English with Mathematics and Graphing Lines (Part 1)

• AlRichards314 video introduction to translating verbal phrases into algebraic expressions

• Examples are given of translating very basic phrases including phrases such as “increased by” and “decreased by”

• Also includes translation of a word problem into a system of two linear equations

• Time 5:19


http://youtu.be/5gThXINIMSY

Link: Writing Expressions

• Khan Academy interactive practice problems on writing simple variable expressions from verbal phrases



https://www.khanacademy.org/math/algebra/introduction-to-algebra/writing-expressions-tutorial/e/writing_expressions_1


• Khan Academy interactive practice problems on writing compound variable expressions from verbal phrases



https://www.khanacademy.org/math/algebra/introduction-to-algebra/writing-expressions-tutorial/e/writing_expressions_2

Link: Writing Expressions with Variables Word Problems

• Khan Academy interactive practice problems on writing variable expressions from word problems



https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-writing-expressions/e/writing-expressions-with-variables-word-problems

Evaluating Variable Expressions• Description and examples of evaluating variable expressions

by substituting specific numbers for the variables• Evaluating Algebraic Expressions• Evaluating Expressions With Two Variables• Evaluating Expressions Where Individual Variable Values are U

nknown • Evaluating Expressions in Word Problems• Interactive Practice Problems: Evaluating Expressions in One V

ariable• Interactive Practice Problems: Evaluating Expressions in Two V

ariables• Interactive Practice Problems: Evaluating Expressions With Var

iables in Word ProblemsReturn to Topics List

CONTENTS:

Link: Evaluating Algebraic Expressions

• Mathispower4u video examples introducing evaluating various types of algebraic expressions at specific numbers

• Defines variable expressions and reviews order of operations• Steps use substitution, order of operations, exponents, and

fractions• Time 7:52

Evaluating Variable Expressions

http://www.youtube.com/watch?v=vQT0e_p_Z8s

Link: Evaluating Expressions With One Variable

• Khan Academy video of very basic examples of evaluating algebraic expressions at specific numbers

• Time 3:21


http://www.youtube.com/watch?v=kS4H-DOIhAE

Link: Example: Evaluating an Expression

• Khan Academy video example of evaluating an algebraic expression at specific numbers

• Time 2:00


https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/variables-and-expressions-1

Link: Expressions With Two Variables

• Khan Academy video examples introducing evaluating expressions in two variables

• Time 1:58


https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/expressions-with-two-variables

Link: Example: Evaluating Expressions With 2 Variables

• Khan Academy video example of evaluating an algebraic expression with two variables at specific numbers

• Time 1:46


https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/evaluating-expressions-with-two-variables

Link: Ex: Evaluate a Variable Expression with Exponents and Fractions

• Mathispower4u video example of substituting values into an expression with exponents and fractions

• Reviews order of operations• 2:33


http://www.youtube.com/watch?v=F2hq2sS9qss

Link: Examples of Evaluating Variable Expressions

• Khan Academy video examples of evaluating algebraic expressions of many types

• Time 12:26


https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/variable-expressions

Link: Evaluating Expressions Where Individual Variable Values are Unknown

• Khan Academy video examples of evaluating variable expressions where relationships between the variables are known but individual variable values are not

• 4:39


https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/exp_unknown_vars/v/evaluating-expressions-where-individual-variable-values-are-unknown

https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/exp_unknown_vars/v/evaluating-expressions-where-individual-variable-values-are-unknown

Link: Evaluating Expressions with Unknown Variables 2

• Khan Academy video examples of evaluating variable expressions where relationships between the variables are known but individual variable values are not

• 3:00


https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/exp_unknown_vars/v/evaluating-expressions-with-unknown-variables-2

Link: Example Evaluating Expressions in Word Problems

• Khan Academy video example of evaluating an algebraic expression in a word problem

• Time 3:24


https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/evaluating-expressions-3-exercise

Link: Evaluating Expressions in One Variable

• Khan Academy interactive practice problems on evaluating algebraic expressions in one variable



https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/e/evaluating_expressions_1

Link: Evaluating Expressions in Two Variables

• Khan Academy interactive practice problems on evaluating algebraic expressions in two variables



https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/e/evaluating_expressions_2

Link: Evaluating Expressions With Variables in Word Problems

• Khan Academy interactive practice problems on evaluating algebraic expressions in word problems



https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/e/evaluating-expressions-3

Simplifying Variable Expressions• Description and examples of using properties of operations

and combining like terms to simplify variable expressions• Combining Like Terms • Equivalent Forms of Expressions • Interactive Practice Problems: Equivalent Forms of ExpressionsReturn to Topics List

CONTENTS:

Link: Combining Like Terms

• Khan Academy video explaining like terms and how to combine like terms

• 4:32

Simplifying Variable Expressions

https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-equivalent-expressions/v/combining-like-terms

Link: Adding Like Rational Terms

• Khan Academy video example of combining two variable expressions with fractions

• 1:14


https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-equivalent-expressions/v/adding-like-rational-terms

Link: Combining Like Terms 1

• Khan Academy video example of combining like terms to simplify an algebraic expression

• 3:06


https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-equivalent-expressions/v/combining-like-terms-1

Link: Combining Like Terms 2

• Khan Academy video example of combining like terms to simplify a complex variable expression

• Reviews commutative property of addition to group like terms by changing the order

• 3:43


https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-equivalent-expressions/v/combining-like-terms-2

Link: Equivalent Forms of Expressions 1

• Khan Academy video with multiple choice examples using properties of operations to find simpler equivalent forms of algebraic expressions

• Reviews the distributive and commutative properties and explains why some of the expressions are not equivalent

• 5:32


https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-equivalent-expressions/v/equivalent-forms-of-expressions-1

Link: Equivalent Forms of Expressions 1

• Khan Academy interactive practice problems on simplifying algebraic expressions using distributive and commutative properties and combining like terms



https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-equivalent-expressions/e/equivalent-forms-of-expressions-1

Polynomial Expressions• Introduction to polynomial expressions, including terminology,

simplifying, adding and subtracting• Definitions and Terminology• Combining Like Terms to Simplify Polynomials• Adding and Subtracting Polynomials• Interactive Practice Problems: Adding and Subtracting Polyno

mials• Operations with Polynomials CalculatorReturn to Topics List

CONTENTS:

Link: Polynomials: Definitions / Evaluation

• Purplemath text lesson on the terminology of polynomials • Includes definitions of term, degree, coefficient, constant term,

leading term, polynomial, and monomial• Also introduces • evaluation of a polynomial at a specific number• simplifying by combining like terms

Polynomial Expressions

http://www.purplemath.com/modules/polydefs.htm

Link: Polynomial Expressions 1 - Explaining Polynomial Expressions

• Tutortag video introducing the terminology of polynomials • Includes definitions of coefficient, polynomial, monomial,

binomial, and trinomial• Time 2:43


http://youtu.be/nMeKGHJP1Tg

Link: Terms, Coefficients, and Exponents in a Polynomial

• Khan Academy video introducing the terminology of polynomials via an example

• Includes identification of terms, coefficients, and exponents • Time 2:36


https://www.youtube.com/watch?v=REiDXCN0lGU

Link: Ex: Intro to Polynomials in One Variable

• Mathispower4u video introducing the terminology of polynomials via an example

• Includes definition of polynomial and identification of terms, degrees, coefficients, leading term, and the degree of a polynomial

• Time 2:59


http://www.youtube.com/watch?v=3u16B2PN9zk

Link: Combining Like Terms

• Mathispower4u video introducing like terms and simplifying polynomials by combining like terms

• Includes definition of like terms and examples of like terms and unlike terms

• Discusses the distributive law and its role in combining like terms, as well as how combining like terms is done in practice

• Includes examples of simplifying polynomials in one or two variables

• Time 4:49


http://www.youtube.com/watch?v=5GDNMfo0PbQ

Link: Simply a Polynomial

• Khan Academy video example of simplifying a polynomial by combining like terms

• Explains the difference between like and unlike terms• Time 3:37


https://www.youtube.com/watch?v=vN0aL-_vIKM

Link: Addition and Subtraction of Polynomials

• Khan Academy video introducing addition and subtraction of polynomials by combining like terms

• Includes an explanation of what a polynomial is, plus terminology such as term, constant term, degree, coefficient, and standard form

• Examples include• addition of polynomials in one variable by combining like terms• subtraction of polynomials in two variables by first distributing

the minus sign and then combining like terms• constructing polynomials representing areas of figures

• Time 15:59


https://www.youtube.com/watch?v=ZgFXL6SEUiI

Link: Simplifying Algebraic Expressions

• Mathispower4u video introducing using the distributive property to clear parentheses and combining like terms in polynomial expressions

• Reviews the distributive property• Reviews multiplicative property of -1 (i.e., -1∙a = -a) and the

opposite of a sum (i.e., distributing a minus sign across a sum)• Includes examples of simplifying expressions• Time 5:24


http://youtu.be/_A8lLbZCrlw

Link: Simplify Polynomial Expressions - Add/Subtract/Multiply

• Mathispower4u video examples of simplifying polynomials• Examples include• adding and subtracting polynomials by clearing parentheses and

combining like terms• distributing a constant across a sum to clear parentheses• distributing a non-constant monomial across a sum

• Time 4:22


http://youtu.be/Gp2dLnaPr7o

Link: Adding and Subtracting Polynomials

• Purplemath text lesson on adding and subtracting polynomials• Includes examples of • adding polynomials (both horizontally and vertically) by clearing

parentheses and combining like terms• subtracting polynomials (both horizontally and vertically) by

distributing the minus sign (or -1) across a sum to clear parentheses and then combining like terms


http://www.purplemath.com/modules/polyadd.htm

Link: How Do You Add Polynomials?

• Virtual Nerd video example of adding polynomials• Gives step-by-step instructions to• rewrite the sum without parentheses• identify the like terms• group like terms• combine like terms• rewrite the sum in standard form

• Time 4:59


http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/add-subtract/add/addition-example

Link: Adding Polynomials

• Mathispower4u video examples of adding polynomials by clearing parentheses and combining like terms

• Time 5:09


http://www.youtube.com/watch?v=KYZR7g7QcF4

Link: How Do You Subtract Polynomials?

• Virtual Nerd video example of subtracting polynomials• Gives step-by-step instructions to• distribute the minus sign to remove parentheses• identify the like terms• group like terms• combine like terms

• Time 2:07


http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/add-subtract/subtract/subtraction-example

Link: Subtracting Polynomials

• Mathispower4u video examples of subtracting polynomials by distributing a -1 to clear parentheses and combining like terms

• Time 4:43


http://www.youtube.com/watch?v=xq-zVm25VC0

Link: Adding and Subtracting Polynomials 1

• Khan Academy video example of adding polynomials by clearing parentheses and combining like terms

• Time 2:01


https://www.youtube.com/watch?v=ahdKdxsTj8E


• Khan Academy video example of subtracting polynomials by distributing a -1 to clear parentheses and combining like terms

• Time 1:43


https://www.youtube.com/watch?v=ZGl2ExHwdak


• Khan Academy video example of adding and subtracting polynomials in one expression by clearing parentheses and combining like terms

• Time 2:27


https://www.youtube.com/watch?v=DMyhUb1pZT0

Link: Practice Adding/Subtracting Polynomials

• Khan Academy interactive practice problems on simplifying sums and differences of polynomials



https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/polynomial_basics/e/adding_and_subtracting_polynomials

Link: Operations with Polynomials Calculator

• Math Portal polynomial operation calculator• Enter two polynomials and the calculator will add, subtract,

multiply, or divide the polynomials as requested• Calculator can also generate examples• A complete step-by-step solution is given if requested


http://www.mathportal.org/calculators/polynomials-solvers/polynomials-operations-calculator.php

Polynomial Multiplication• Description and examples of multiplying polynomials,

including special products• Multiplying Monomials• Multiplying Monomials by Polynomials • Multiplying Binomials; FOIL Method• Special Products of Binomials: Squares and Conjugates• Multiplying a Binomial and a Trinomial• General Multiplication of Polynomials• Interactive Practice Problems: Multiplying Simple Polynomials• Interactive Practice Problems: Multiplying General Polynomial

s• Operations with Polynomials CalculatorReturn to Topics List

CONTENTS:

Link: Multiplying Monomials

• Mathispower4u video examples of multiplying monomials and raising a monomial to a power using the laws of exponents

• Time 2:53

Polynomial Multiplication

http://www.youtube.com/watch?v=30x8hY32B0o

Link: How Do You Multiply Monomials?

• Virtual Nerd video example simplifying a product of three monomials in two variables by regrouping the factors and using laws of exponents

• Time 1:20


http://www.virtualnerd.com/algebra-1/exponents-exponential-functions/monomials-polynomials/monomials/monomial-multiplication-example

Link: Multiplying Monomials by Polynomials

• Khan Academy video example of multiplying a monomial by a trinomial, using the distributive property and laws of exponents

• Time 2:43


https://www.youtube.com/watch?v=pD2-H15ucNE

Link: How Do You Multiply a Monomial by a Polynomial?

• Virtual Nerd video example of multiplying a monomial by a trinomial in two variables, using the distributive property and laws of exponents

• Time 1:27


http://www.virtualnerd.com/algebra-1/exponents-exponential-functions/monomials-polynomials/polynomials/monomial-by-polynomial-multiplication

Link: Ex: Multiplying Using the Distributive Property

• Mathispower4u video examples of multiplying monomials by polynomials, using the distributive property and laws of exponents

• Time 2:54


http://www.youtube.com/watch?v=bwTmApTV_8o

Link: Simple Polynomial Multiplication

• Purplemath text lesson introducing multiplication of polynomials

• Topics and examples include• multiplication of monomials using laws of exponents• multiplication of a monomial by a polynomial using the

distributive law and laws of exponents• multiplication of two binomials horizontally using the distributive

law, vertically, and using the “FOIL” method• multiplication of polynomials with more than two terms

horizontally and vertically


http://www.purplemath.com/modules/polymult.htm

Link: FOIL for Multiplying Binomials

• Khan Academy video example of multiplying two binomials, first using the “FOIL” method and then using the distributive law twice

• Time 5:47


https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying-binomials/v/multiplying-binomials

Link: Multiplying Binomials

• Mathispower4u video examples of multiplying two binomials using the distributive property and the “FOIL” method

• Time 4:12


http://www.youtube.com/watch?v=W-X4SSeIjsY

Link: Special Products of Binomials

• Khan Academy video on squaring binomials and the product of a sum and a difference of two terms

• Topics include both specific examples and general formulas for• the square of a binomial• the product of the sum of two terms and the difference of the

same two terms• Time 10:36


https://www.youtube.com/watch?v=bFtjG45-Udk

Link: Ex: Squaring Binomials

• Mathispower4u video examples of squaring binomials by using the standard methods for multiplying binomials

• Also introduces formulas for squaring binomials without examples

• Time 3:22


http://www.youtube.com/watch?v=l7ivdpf4XnQ

Link: Ex: Multiplying Binomial Conjugates - Special Binomial Products

• Mathispower4u video examples of the product of the sum of two terms and the difference of the same two terms using the standard methods for multiplying binomials

• Also defines conjugates and introduces the formula for a product of conjugates without examples

• Time 2:54


http://www.youtube.com/watch?v=hBASaFceZxY

Link: Special Products of Polynomials 1

• Khan Academy video on the product of the sum of two terms and the difference of the same two terms

• Derives and explains a general formula for such a product• Includes an example using the formula• Time 2:29


https://www.youtube.com/watch?v=h6HmHjkA034

Link: Ex: Polynomial Multiplication Involving Binomials and Trinomials

• Mathispower4u video examples of multiplying polynomials• Examples are• product of three factors: a monomial and two binomials• product of a binomial and a trinomial

• Time 3:35


http://www.youtube.com/watch?v=bBKbldmlbqI

Link: Multiplying Polynomials

• Khan Academy video example multiplying a binomial by trinomial first horizontally using the distributive law twice, and then vertically

• Time 5:46


https://www.youtube.com/watch?v=yJzLYa-_Y1k

Link: More Multiplying Polynomials

• Khan Academy video example multiplying a binomial by trinomial using the distributive law twice

• Time 2:34


https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying_polynomials/v/more-multiplying-polynomials

Link: Multiplying Polynomials 3

• Khan Academy video example multiplying a binomial by trinomial using the distributive law twice

• The product of the polynomials is introduced as representing a volume

• Time 4:19


https://www.youtube.com/watch?v=bamcYQDzVTw

Link: Multiplication of Polynomials

• Khan Academy video examples of multiplying various types of polynomials

• Types of examples include• monomial times polynomial• binomial times binomial• binomial times trinomial, multiplied vertically

• Time 9:49


https://www.youtube.com/watch?v=fGThIRpWEE4


• Khan Academy interactive practice problems on multiplying simple polynomials



https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying_polynomials/e/multiplying_polynomials_0.5


• Khan Academy interactive practice problems on multiplying more complicated polynomials



https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying_polynomials/e/multiplying_polynomials

Polynomial Division• Description and examples of dividing polynomials, including

long division and synthetic division• Polynomial Divided by a Monomial• Long Division of Polynomials• Synthetic Division• Operations with Polynomials CalculatorReturn to Topics List

CONTENTS:

Link: Polynomial Divided by a Monomial

• Khan Academy video example dividing a polynomial by a monomial using the distributive property and laws of exponents

• Time 4:44

Polynomial Division

https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/dividing_polynomials/v/polynomial-divided-by-monomial

Link: Ex: Divide a Polynomial by a Monomial

• Mathispower4u video examples dividing a polynomial by a monomial using the distributive property and laws of exponents

• Time 2:43

Polynomial Division

http://www.youtube.com/watch?v=AIjELHgv7xE

Link: Polynomial Division

• Purplemath text lesson on dividing polynomials• Topics and examples include• Dividing a polynomial by a monomial• Factoring and “cancelling” (reducing a fraction)• Long division, with and without a remainder

Polynomial Division

http://www.purplemath.com/modules/polydiv.htm

Link: Polynomial Division: Long Division

• Mathispower4u video of long division of a polynomial by a binomial

• Includes• review of long division of numbers• written procedure for long division of polynomials explained with

an example• further examples dividing a polynomial by a binomial

• Time 9:25

Polynomial Division

http://www.youtube.com/watch?v=brpNxPAkv1c

Link: Polynomial Division

• Khan Academy video examples of long division of polynomials with remainders

• Time 12:09

Polynomial Division

https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/dividing_polynomials/v/polynomial-division

Link: Algebraic Long Division

• Khan Academy video with a (long) example of long division of polynomials

• Time 10:21

Polynomial Division

http://youtu.be/4u8_AMacu-Y

Link: How to do Long Division with Polynomials

• Mathbff video examples of long division of polynomials with remainders

• Includes polynomials with “missing” terms• Time 11:13

Polynomial Division

http://www.youtube.com/watch?v=Ih1wb6AxhMI

Link: Divide a Polynomial by a Degree Two Binomial

• Mathispower4u video example of long division of a polynomial by a degree two binomial with a remainder

• Time 4:14

Polynomial Division

http://www.youtube.com/watch?v=P6OTbUf8f60

Link: Dividing Polynomials with Remainders

• Khan Academy video example of long division of polynomials with a remainder

• Includes a dividend with a “missing” term (i.e., 0 coefficient)• Includes checking the answer by multiplying and simplifying• Time 6:23

Polynomial Division

https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/dividing_polynomials/v/dividing-polynomials-with-remainders

Link: Polynomial Division: Synthetic Division

• Mathispower4u video introducing synthetic division of a polynomial by a binomial of the form x – k

• Includes • general explanation of the method of synthetic division • several explicit examples• example where the coefficient of x in the divisor is not 1

• Time 10:07

Polynomial Division

http://www.youtube.com/watch?v=5dBAdzl2Mns

Link: Synthetic Division

• Khan Academy video explaining synthetic division of a polynomial by a binomial of the form x + k via an example

• Time 5:21

Polynomial Division

https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/dividing_polynomials/v/synthetic-division

Link: How to Do Synthetic Division

• Mathbff video explaining synthetic division of a polynomial by a binomial of the form x - k via an example

• Time 6:35

Polynomial Division

http://youtu.be/lLgRS0mUZLw

Link: Synthetic Division, Example 2

• Khan Academy video example of synthetic division of a polynomial by a binomial of the form x - k

• Includes a dividend with a “missing” term (i.e., 0 coefficient)• Time 5:00

Polynomial Division

https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/dividing_polynomials/v/synthetic-division-example-2

Link: Ex 2: Divide a Polynomial by a Binomial Using Synthetic Division

• Mathispower4u video example of synthetic division of a polynomial by a binomial of the form x + k

• Time 3:22

Polynomial Division

http://www.youtube.com/watch?v=_Y0fRbh1RY8


• Mathispower4u video example of synthetic division of a polynomial by a binomial of the form x - k


Polynomial Division

http://www.youtube.com/watch?v=h1oSCNuA9i0


• Mathispower4u video example of synthetic division of a polynomial by a binomial of the form x + k


Polynomial Division

http://www.youtube.com/watch?v=bqm4DoznJxo




Polynomial Division


Factoring Polynomials• Description and examples of factoring polynomials, including special

forms and factoring by grouping• Greatest Common Factor of Monomials• Factoring the GCF of Terms Out of a Polynomial • Factoring a Difference of Squares• Factoring a Sum or Difference of Cubes• Factoring Perfect Square Trinomials• Factoring Quadratic Polynomials and Trinomials• Interactive Practice Problems: Factoring Quadratics with Leading Coe

fficient 1 • Interactive Practice Problems: Factoring Quadratics with Leading Coe

fficient Not 1 • Factoring by Grouping• Interactive Practice Problems: Factoring by GroupingReturn to Topics List

CONTENTS:

Link: How Do You Find the Greatest Common Factor of Monomials?

• Virtual Nerd video example finding the greatest common factor of 4 monomials in 2 variables

• Steps used in the example to find the GCF are• factor each monomial• identify common factors• list the common factors• multiply the common factors

• Time 3:52

Factoring Polynomials

http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factors-and-greatest-common-factors/greatest-common-factors/greatest-common-factor-monomials

Link: Monomial Greatest Common Factor

• Khan Academy video example finding the greatest common factor of 2 monomials in 2 variables

• Time 3:13


https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/multiplying%20monomials/v/monomial-greatest-common-factor

Link: Factor Expressions Using the GCF

• Khan Academy video example of factoring the greatest common factor of the terms out of a binomial in two variables

• Begins with a review of finding the GCF of two monomials• Time 5:28


https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/Factoring-simple-expressions/v/factor-polynomials-using-the-gcf

Link: Ex 1: Identify GCF and Factor a Binomial

• Mathispower4u video examples of factoring the greatest common factor of the terms out of binomials

• Includes finding the GCF of the terms• Time 4:16


http://www.youtube.com/watch?v=25_f_mVab_4

Link: Ex 2: Identify GCF and Factor a Trinomial

• Mathispower4u video examples of factoring the greatest common factor of the terms out of trinomials



http://www.youtube.com/watch?v=3f1RFTIw2Ng

Link: How Do You Factor the Greatest Common Factor Out of a Polynomial?

• Virtual Nerd video example of factoring the greatest common factor of the terms out of a polynomial in two variables



http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factors-and-greatest-common-factors/greatest-common-factors/greatest-common-factor-example

Link: Simple Polynomial Factoring

• Purplemath text lesson on basic polynomial factoring techniques

• Topics and examples include• factoring out the greatest common factor of the terms• factoring by grouping (referred to here as “factoring in pairs”) for

quadratics


http://www.purplemath.com/modules/simpfact.htm

Link: How Do You Know if You Have a Difference of Squares?

• Virtual Nerd video explaining how to identify a binomial as a “difference of squares’’

• Two issues to be aware of:• considers only binomials with perfect square coefficients• the condition “the degree of each term must be even or 0” is true

but slightly misleading, since 0 is even• Time 2:26


http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-special-products/difference-square-or-cubes/difference-of-squares-identification

Link: How Do You Factor a Polynomial Using Difference of Squares?

• Virtual Nerd video example giving a step-by-step procedure to factor a binomial that is a difference of squares

• Time 4:45


http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-special-products/difference-square-or-cubes/difference-of-squares-example

Link: Factoring a Difference of Squares

• Mathispower4u video introducing the factoring of a difference of squares

• Video includes• identifying a difference of squares• general formula for the factors of a difference of squares• numerous examples from very basic to somewhat more advanced

• Time 5:25


http://www.youtube.com/watch?v=0yBDsZvfT0g

Link: Example: Factor a Difference of Squares

• Mathispower4u video examples of factoring difference of squares binomials

• Includes review of the formula for the factors of a difference of squares and several examples

• Time 4:19


http://www.youtube.com/watch?v=Li9IBp5HrFA

Link: Ex: Factor a Difference of Squares with a Common Factor

• Mathispower4u video example of factoring a difference of squares binomial in which the terms have a (perfect square) common factor

• Time 3:06


http://www.youtube.com/watch?v=-D8rtYiXaZY&feature=youtu.be

Link: Factoring a Sum or Difference of Cubes

• Mathispower4u video introducing factoring of sum of cubes and difference of cubes binomials

• Video includes• general formulas for factors of sum and difference of cubes

binomials• verification of sum of cubes formula using long division • examples, including one in which the terms of the binomial have

a common factor• Time 6:07


http://www.youtube.com/watch?v=5KyxD6qg3g8

Link: How Do You Factor a Polynomial Using a Sum of Cubes?

• Virtual Nerd video example giving a step-by-step procedure for factoring a sum of cubes binomial

• Time 4:15


http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-special-products/difference-square-or-cubes/sum-of-cubes

Link: How Do You Factor a Polynomial Using a Difference of Cubes?

• Virtual Nerd video example giving a step-by-step procedure for factoring a difference of cubes binomial

• Time 4:40


http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-special-products/difference-square-or-cubes/difference-of-cubes

Link: Ex 1: Factor a Sum or Difference of Cubes

• Mathispower4u video examples of factoring a sum of cubes binomial and a difference of cubes binomial

• Video includes• brief review of formulas for factors of sum and difference of

cubes• a basic example of each type

• Time 3:19


http://www.youtube.com/watch?v=tFSEpOB262M&feature=youtu.be


• Mathispower4u video examples of factoring a sum of cubes binomial and a difference of cubes binomial


cubes• an example of each type in which the terms of the binomial have

a common factor• Time 3:35


http://www.youtube.com/watch?v=JzJNgLK7Vd0&feature=youtu.be


• Mathispower4u video example of factoring a sum of cubes binomial


cubes• an example of a sum of cubes in which the terms of the binomial

have a perfect cube common factor and relatively large coefficients

• Time 5:23


http://www.youtube.com/watch?v=J_0ctMrl5_0&feature=youtu.be

Link: Factoring Perfect Square Trinomials & the Difference of Two Squares

• AlRichards314 video on factoring trinomials that are squares of binomials and factoring difference of squares binomials

• Video includes• review of formulas for the square of a binomial and the product

of a sum of two terms and the difference of the same terms• product formulas reinterpreted as factoring formulas• several examples of each type

• Time 7:45


http://youtu.be/GlSY4xzfjvE

Link: Factoring a Perfect Square Trinomial

• Mathispower4u video on factoring trinomials that are squares of binomials

• Video includes• how to recognize a perfect square trinomial• formula for the factors of a perfect square trinomial• several examples, including one in which the terms of the

trinomial have a common factor• Time 7:52


http://www.youtube.com/watch?v=1_kxLXFtqHg

Link: How Do You Use a Shortcut to Factor a Perfect Square Trinomial?

• Virtual Nerd video on factoring trinomials that are perfect squares of binomials

• Video includes• how to recognize the pattern of a perfect square trinomial• formula for the factors of a perfect square trinomial (the

“shortcut”)• an example, using the formula and a step-by-step procedure

• Time 8:10


http://www.virtualnerd.com/algebra-1/polynomials-and-factoring/factoring-special-products/perfect-square-trinomials/perfect-square-trinomial-shortcut

Link: Ex: Factor a Perfect Square Trinomial

• Mathispower4u video examples of the special case of factoring quadratic polynomials that are perfect square trinomials

• Does not rely on memorized formula for factoring; instead uses a modified “trial and error” method given that the degree 2 and constant terms are perfect squares

• Time 5:33


http://www.youtube.com/watch?v=x-IcA-fV_Lk

Link: Factoring Quadratics

• Purplemath text lesson on factoring quadratic polynomials• Topics and examples include• the “simple case” where the leading coefficient is 1• the “hard case” where the leading coefficient is not 1, using both

the “trial and error” method and the “box method”• the “weird case” of quadratic type polynomials that are not

actually quadratic


http://www.purplemath.com/modules/factquad.htm

Link: Factoring Trinomials with a Leading 1

• Khan Academy video example of factoring a quadratic polynomial with leading coefficient 1

• Video includes an explanation of what to look for (and why) in the coefficients of the quadratic in order to find the factors

• Method is illustrated with an example• Time 4:12


http://youtu.be/nOZTe8jU2g4

Link: Factoring a Trinomial with Leading Coefficient of 1 - The Basics

• Mathispower4u video examples of factoring a quadratic polynomial with leading coefficient 1


• Method is illustrated with numerous examples, including one in which the terms of a trinomial have a common factor

• Time 10:34


http://www.youtube.com/watch?v=6SACul2TFEM

Link: Factoring Quadratic Expressions

• Khan Academy video examples of factoring a quadratic polynomial with leading coefficient 1


• Method is illustrated with many examples, including one in which the terms of a trinomial have a common factor

• Time 16:30


https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/v/factoring-quadratic-expressions

Link: Factoring Trinomials: Trial and Error and Grouping

• Mathispower4u video examples of factoring a quadratic polynomial where the leading coefficient is not 1

• Video includes• trial and error (or reverse FOIL) method with an explanation of

the procedure and several examples• grouping method with several examples

• Time 9:45


http://www.youtube.com/watch?v=55wm2c1xkp0

Link: Factoring ax^2+bx+c (Part 1)

• AlRichards314 video examples of factoring a quadratic polynomial where the leading coefficient is not 1

• Method used is a combination of trial and error (or reverse FOIL) and grouping

• Part 2 includes more examples• Time 5:22


http://youtu.be/1v3ry7v1QQ4

Link: Factoring ax^2+bx+c (Part 2)

• AlRichards314 video examples of factoring a quadratic polynomial where the leading coefficient is not 1


• Continuation of Part 1 with more examples• Time 4:49


http://youtu.be/9LQ-cTE7nuE

Link: Factoring Trinomials with a Common Factor

• Khan Academy video example of factoring a quadratic polynomial in which the terms have a numerical common factor


• Time 5:01


https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/v/factoring-trinomials-with-a-common-factor

Link: Practice: Factoring Quadratics 1

• Khan Academy interactive practice problems on factoring quadratic polynomials with leading coefficient 1



https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/e/factoring_polynomials_1

Link: Practice: Factoring Quadratics 2

• Khan Academy interactive practice problems on factoring quadratic polynomials where the leading coefficient is not 1



https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-quadratic-expressions/e/factoring_polynomials_2

Link: Factor by Grouping

• Mathispower4u video examples of factoring polynomials using the grouping method

• Video includes• introduction to the grouping method via an example• written description of the steps in the grouping method• several examples of factoring cubic polynomials by grouping• example using grouping to solve a quadratic equation by

factoring• Time 7:48


http://www.youtube.com/watch?v=15suKxAV1ow

Link: Ex: Factor a Polynomial Using the Grouping Technique

• Mathispower4u video examples of factoring cubic polynomials using the grouping method

• Time 3:51


http://www.youtube.com/watch?v=wwSgwxpMThQ

Link: Factoring by Grouping and Factoring Completely

• Khan Academy video examples of factoring quadratic polynomials using the grouping method

• Includes an example of a trinomial in which the terms have a common factor

• Time 13:57


https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-by-grouping/v/factor-by-grouping-and-factoring-completely

Link: Example: Basic Grouping

• Khan Academy video example of factoring an expression with 4 terms in 2 variables using the grouping technique

• Time 3:46


https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-by-grouping/v/factoring-trinomials-by-grouping-1

Link: Factoring Polynomials

• The Cool Math Guy video examples of factoring polynomials• Video includes• factoring out the greatest common factor of the terms• factoring quadratic polynomials• factoring by grouping

• Time 9:56


http://youtu.be/HinoXYey2n4

Link: Practice: Factoring Polynomials by Grouping

• Khan Academy interactive practice problems on factoring polynomials using the grouping technique



https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/factoring-by-grouping/e/factoring_polynomials_by_grouping_1

Formulas & Polynomials in Two (or more) Variables• Description and examples of formulas and polynomial

equations, including evaluation at specific numbers and solving for one variable in terms of the others

• Equations and Formulas• Writing a Polynomial Expression from a Verbal Phrase • Evaluating Formulas and Polynomials for Specific Values of the

Variables• Solving for One Variable in Terms of the Others in a Formula• Interactive Practice Problems: Solving Equations in Terms of a

Variable Return to Topics List

CONTENTS:

Link: Equations and Formulas

• Math Is Fun text lesson on equations, formulas, and the difference between them

Formulas & Polynomials in Two (or more) Variables

http://www.mathsisfun.com/algebra/equation-formula.html

Link: Example Question Involving Polynomials

• Tutortag video example of translating a verbal phrase into a polynomial expression

• Example expresses the difference in areas between two geometric figures whose dimensions are given as variables

• Time 5:34


http://www.youtube.com/watch?v=6CICoewLXWs

Link: Evaluate a Formula Using Substitution

• Khan Academy video example using substitution in a formula to convert degrees Celsius to degrees Fahrenheit

• Time 1:15


https://www.khanacademy.org/math/algebra/introduction-to-algebra/variable-and-expressions/v/evaluate-a-formula-using-substitution

Link: Evaluating a Polynomial at a Given Value

• Khan Academy video example of substitution of a negative number in a quadratic polynomial expression

• Time 1:09


https://www.khanacademy.org/math/algebra/multiplying-factoring-expression/polynomial_basics/v/evaluating-a-polynomial-at-a-given-value

Link: How Do You Evaluate an Algebraic Expression by Plugging in Values?

• Virtual Nerd video example of evaluating a polynomial expression in two variables at given values of the variables

• Time 1:07


http://www.virtualnerd.com/algebra-1/algebra-foundations/variables-expressions/algebraic-expressions/plugging-variables-into-expressions

Link: Polynomial Expressions and Polynomial Functions

• Mathispower4u video examples of substitution of numbers in polynomial expressions

• Video includes• review of polynomial terminology• examples of evaluation of polynomials in more than one variable

at specific values of the variables• evaluation of polynomial expressions in one variable at specific

numbers both by hand and using a graphing calculator• Time 7:25


http://youtu.be/aPTg9Obk-2A

Link: Evaluate a Quadratic Equation - Death Application

• Mathispower4u video example evaluating a quadratic polynomial at a number

• Polynomial formula models a real-world problem and includes non-integer (decimal) coefficients

• A calculator is used for most of the calculations• Time 4:52


http://www.youtube.com/watch?v=dEZk4MiHg1Y&feature=youtu.be

Link: Evaluate a Polynomial Equation - Flu Virus Application

• Mathispower4u video example evaluating a fourth degree polynomial at a number

• Polynomial formula models a real-world problem and includes non-integer (decimal) coefficients

• A calculator is used for some of the calculations• Time 4:01


http://www.youtube.com/watch?v=q30UXqma5Qs&feature=youtu.be

Link: Solving Equations and Formulas

• Slide Share text slides with examples of formulas in more than one variable and solving for one variable in terms of the others

• Emphasizes “undoing” operations to isolate the desired variable


http://www.slideshare.net/kdwilliams/solving-equations-and-formulas

Link: Solving Literal Equations

• Purplemath text lesson on solving for one variable in terms of the others in a formula with two or more variables

• Topics and examples include• geometric and other types of formulas in three or more variables• rewriting a linear equation in slope-intercept form to find the

slope of the line


http://www.purplemath.com/modules/solvelit.htm

Link: Rearrange Formulas to Isolate Specific Variables

• Khan Academy video example solving the area of a triangle formula for the height in terms of the area and base

• Time 2:29


https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/solving_for_variable/v/rearrange-formulas-to-isolate-specific-variables

Link: Solving for a Variable

• Khan Academy video example solving the rectangle perimeter formula for the length in terms of the perimeter and width

• Time 1:24


https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/solving_for_variable/v/solving-for-a-variable

Link: Example: Solving for a Variable

• Khan Academy video example solving the rectangle perimeter formula for the width in terms of the perimeter and length

• Problem is solved in various ways• Time 6:58


https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/solving_for_variable/v/example-of-solving-for-a-variable

Link: Solving for a Variable 2

• Khan Academy video example solving for the Fahrenheit temperature in the formula giving the Celsius temperature in terms of the Fahrenheit temperature

• Time 2:41


https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/solving_for_variable/v/solving-for-a-variable-2

Link: Solving Equations in Terms of a Variable

• Khan Academy interactive practice problems on solving for one variable in terms of the others in an equation in two or more variables

• A sequence of five practice problems is provided, along with• hints to help solve the problem, if needed• links to video lessons if you get stuck


https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/solving_for_variable/e/solving_for_a_variable

Polynomial Functions• Description and examples of the behavior of polynomial

functions, including end behavior, smoothness, turning points, and graphs

• End Behavior of Polynomial Function• General Properties of Polynomial FunctionsReturn to Topics List

CONTENTS:

Link: Summary of End Behavior of Polynomial Function

• Mathispower4u video describing the end (or long run) behavior of a polynomial in terms of the degree and the sign of the leading coefficient

• Time 5:48

Polynomial Functions

http://www.youtube.com/watch?v=y78Dpr9LLN0&feature=youtu.be

Link: How Polynomials Behave

• Math Is Fun text lesson on the behavior of the graphs of polynomial functions

• Topics and examples include• continuity and smoothness• behavior of xn for even and odd values of n• behavior of axn for various values of a• turning points• end behavior


http://www.mathsisfun.com/algebra/polynomials-behave.html

Link: Polynomial Graphs: General Behavior

• Purplemath text lesson on the behavior of the graphs of polynomial functions

• Topics and examples include• end behavior• zeroes and their multiplicities• degrees and turning points• quick graphing


http://www.purplemath.com/modules/polyends.htm

Link: Characteristics of Polynomial Functions

• AlRichards314 video introduction to the behavior of graphs of polynomial functions

• Topics and examples include• general shape of graphs of linear, quadratic, cubic, and quartic

polynomials• using finite differences to determine the degree of a polynomial

given by a table of values• Time 9:53


http://youtu.be/wEdK4NAy4sw

Link: How to Graph Polynomials

• For Dummies text lesson on graphing polynomial functions• Topics and examples include• plotting the intercepts• end behavior• determining whether the graph is below or above the axis

between each pair of intercepts• sketching the graph


http://www.dummies.com/how-to/content/how-to-graph-polynomials.html

polynomials, expressions, and formulas or, how i learned to stop worrying and love the variable

Documents

properties of numbers

examples of numbers

irrational numbers time

natural numbers

study of numbers

irrational numbers subsets

real numbers subsets

set of real numbers