algebra ii chapter 5 - mrs. gruver's classroom website -...
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Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Algebra IIChapter 5:
Polynomials and Polynomial Functions
Part 1
Vocabulary
Chapter 5 Lesson 1Use Properties of Exponents
Learn these!
Love these!
Know these!
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 1: Evaluate Numerical Expressions
State which property of exponents you are using!
Example 2: Use Scientific Notation in Real Life
Scientific Notation Reminder:The first number must be a number between 1 and 9.99!10 X 100 = 1.0 X 101 (when you divide on the le, then you mulply on the right)0.1 X 100 = 1.0 X 10‐1 (when you mulply on the le, then you divide on the right)
When dividing or multiplying scientific notation:1. Divide or multiply the number parts and get a result. Round to 2
decimal places!2. Use the Quotient of Powers Property or Product of Powers to deal
with the exponent parts!3. Check to make sure the number is written in scientific notation!!!
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 3: Simplify ExpressionsIn simplified form, all exponents should be positive!
State which properties of exponents you are using!
Example 4: Standardized Test PracticeSimplify. State which properties of exponents you are using!
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 5: Compare RealLife Volumes
Chapter 5 Lesson 2Evaluate and Graph Polynomial Functions
Vocabulary
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 1: Identify Polynomial FunctionsHow to determine if it is a polynomial function:1. exponent must be a whole number (0,1,2...no negative numbers)2. coefficients must be real numbers3. terms must be monomials (no term can be divided by a variable)
Example 2: Evaluate by Direct Substitution
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 3: Evaluate by Synthetic Substitution
Example 4: Standardized Test Practice
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 5: Graph Polynomial Functions
Use synthetic substitution to save time!
State the domain and range.
Domain:
Range:
Example 6: Solve a MultiStep Problem
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Chapter 5 Lesson 3Add, Subtract, and Multiply PolynomialsVocabulary
Reminder:
Like Terms
Example 1: Add Polynomials1. Combine Like Terms
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 2: Subtract Polynomials 1. Distribute the Negative!!!!
2. Combine Like Terms
Example 3: Multiply Polynomials1. Distribute each term in the first polynomial to each term in the second polynomial
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 4: Multiply Three Binomials1. FOIL the first two binomials
2. Multiply the result by the last binomial
Example 5: Use Special Product Patterns
Reminders:a comes from the first term (always +)b comes from the second term (always +)
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 6: Use Polynomial Models
Chapter 5 Lesson 4Factor and Solve Polynomial Equations
Vocabulary
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 1: Find a Common Monomial Factor
Example 2: Factor the Sum or Difference of Two Cubes
Reminders:a comes from the first term (always +)b comes from the second term (always +)
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 3: Factor by GroupingHow to factor by grouping:1. Check if the polynomial has 4 terms!2. Factor out a common monomial to one set of terms. Do the same with the other set. You must be left with a common binomial for this to work!!! At times, you may need to factor out a negative common monomial!3. Rewrite the common binomial ONCE! Create the new binomial using the factored out pieces.4. Make sure to check if there can be any other factoring completed!
Example 4: Factor Polynomials in Quadratic Form1. Always look for common factors first.2. Check for quadratic form.
*If the first exponent is twice the second exponent, then you can treat it similarly to the factoring we did in chapter 4.
*You might also notice a special pattern that you could use (difference of squares, etc.). *Make sure you make the exponents on the variables correct!
3. Make sure to check if any other factoring can be completed!
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Example 5: Standardized Test PracticeHow to Find the Solutions of Polynomials:1. Factor first. Use all the methods we have discussed in this lesson!2. Set each binomial equal to zero. Don't forget to put any variable pieces equal to
zero as well!3. Solve for all variables.4. Check with your graphing calculator!
Hint: the degree of the polynomial lets you know the number of zeroes that you are searching for (we will discuss the imaginary ones on the next example)
Hint: the degree is 5 so we are searching for 5 zeroes!
Example 6: Solve Polynomial Equations
Alg II Chapter 5 Notes Part 1.notebook
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November 09, 2015
Factoring Ideas to Think About:*Check for a common monomial!*If the polynomial has only 2 terms, check for perfect cubes or perfect squares!*If the polynomial has a degree of 2, think XBox!*If the polynomial has 4 terms, check if you can factor by grouping.*If the first term's exponent is double the second term's exponent, check if it is quadratic form and try XBox! *If, after factoring, any exponent is more than 1, always check again to see if you can factor again!