lecture 1.1 to 1.3 bt

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MAT153

College Math and Statistics

BRAD THOMPSON

Class Meets: M,W E318

8:30 – 10:20

Today’s Agenda

• Syllabus

• Course Information

• Class Procedures

• Questions?

• Sections 1.1 – 1.3

MyLabsPlus Homework

www.dtcc.mylabsplus.com

Login is same as DTCC.

Simplifying / Evaluating Expressions

“P.E.M.D.A.S.”

Evaluate each expression

1. 4 − 5 ∙ 6 + 6 2. 8 − −4 2 − −12

3. 2 3−7 +4 8

4 −3 + −3 −24.

62−3 25

62+13

Evaluating Variable Expressions

*Note: Use parentheses when substituting

1) −𝑥2 − 2𝑥 + 3

2) 𝑥2 − 2𝑥 + 3

3) −𝑥2 − 2𝑥 + 3

4) 𝑥2 − 2𝑥 + 3

3xlet 3xlet

Inequality / Interval Notation

−5 < 𝑥 < 4

−5 < 𝑥 ≤ 4

𝑥 ≥ 3

𝑥 < 2

)4,5(

]4,5(

),3[

)2,(

Absolute Value

0||

0||

,

xifxx

xifxx

xnumberrealanyfor

Absolute Value

|6| |6|

|43| |2|

|48| |85|

6 6

7 2

4 13

Properties of Exponents

yxx 23 25 yx

Properties of Exponents

25xy 2225 yx

Properties of Exponents

23 )6( yx 2636 yx

Properties of Exponents

05 0x

Anatomy of a Polynomial

coefficients

423 2 xx

Degree = highest exponent

constant

term

Polynomials

Polynomial DegreeLeading

Coefficient

Constant

Term

𝟒𝒙𝟓 − 𝟐𝒙𝟑 + 𝟑𝒙 − 𝟗

−𝟓𝒙𝟒 + 𝟑𝒙𝟐 +𝟏

𝟑

𝒙𝟐 − 𝟐𝒙𝟑 + 𝟒𝒙

−𝟏𝟕

5 4 -9

4 -5 1/3

3 -2 0

0 -17 -17

Adding and Subtracting Polynomials

−2p3 − 5p + 7 + −4p2 + 8p + 2

3y3 + 9y2 − 11y + 8 − −4y2 + 10y − 6

Multiplying Polynomials

Use the Properties of exponents

and the Distributive Property

Multiplying Polynomials

Find each of the given products.

2a 4a2 − 6a + 8

Multiplying Polynomials

Find each of the given products.

2k + 3 4k3 − 3k2 + k

Multiplying Polynomials

Multiplying Polynomials

Multiply.

8r + 3 r − 1

Greatest Common Factor

Find the GCF of

12, 27, & 36

Greatest Common Factor

Find the GCF of

15𝑥3, 12𝑥, & 9𝑥2

Factoring

Can think of factoring as

the opposite of

distributing(multiplying).

This means that we’re

actually dividing.

Factoring

“What is common to

all terms that we can

take out?”

Greatest Common Factor

Factor out the greatest common factor.

5𝑦 − 15𝑥𝑦 3𝑥 + 7 5 − 4 3𝑥 + 7 3

Greatest Common Factor

Factor out the greatest common factor.

5𝑥3 + 55𝑥2 + 10𝑥 3 𝑥 + 6 2 + 6 𝑥 + 6 4

Factoring Quadratics

Polynomials of degree 2

mm

x

xx

43

9

946

2

2

2

?

Factoring Quadratics

This can be thought of as the

reverse of “F.O.I.L.”

And you can always check

your answer!

Factoring Quadratics

𝑦2 + 8𝑦 + 12

Factoring Quadratics

𝑥2 + 4𝑥 − 5

Factoring Quadratics

15𝑢2 + 4𝑢 − 4

Factoring Quadratics

12𝑦2 + 7𝑦 − 10

Factoring Quadratics

35 2 xx

Factoring Polynomials

Special CasesDifference of Squares (p. 24)

𝑥2−𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦

𝑥2 − 25

Factoring Polynomials

Special CasesDifference of Squares

𝑥2 − 𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦

9𝑝2 − 16

Factoring Polynomials

Special CasesDifference of Squares

𝑥2 − 𝑦2 = 𝑥 + 𝑦 𝑥 − 𝑦

49𝑎2 + 9

Chapter 1 Exam

• Monday 1/26

–Covers 1.1 – 1.7

Classwork / Homework

• Classwork

–Page 71: 15 – 47 odd

• Homework

– MyLabsPlus HW1

»Due Sunday 1/18, 11:59pm

• Read 1.4, 1.5

• Quiz Wednesday(extra credit)