1 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-1

Polynomials and Polynomial Functions

Chapter 5

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-2

5.1 – Addition and Subtraction of Polynomials

5.2 – Multiplication of Polynomials

5.3 – Division of Polynomials and Synthetic Division

5.4 – Factoring a Monomial from a Polynomial and Factoring by Grouping

5.5 – Factoring Trinomials

5.6 – Special Factoring Formulas

5.7-A General Review of Factoring

5.8- Polynomial Equations

Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-3

§ 5.6

Special Factoring Formulas

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-4

Difference of Two Squares

a2 – b2 = (a + b) (a – b)

Example:a.) Factor x2 – 16.

x2 – 16 = x2 – 42 = (x + 4)(x – 4)

b.) Factor 25x2 – 36y2.25x2 – 36y2 = (5x)2 – (6y)2 =

(5x + 6y)(5x – 6y)

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-5

Factor Perfect Square Trinomials

a2 + 2ab + b2 = (a + b)2

a2 – 2ab + b2 = (a – b)2

Example:a.) Factor x2 – 8x + 16.To determine whether this is a perfect

square trinomial, take twice the product of x and 4 to see if you obtain 8x.

2(x)(4) = 8xx2 – 8x + 16 = (x – 4)2

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-6

Sum of Two Cubes

a3 + b3 = (a + b) (a2 – ab + b2)

Example:a.) Factor the sum of cubes x3 + 64.

)164)(4(

]4)4()[4(4

))((

2

2233

2233

xxx

xxxx

babababa

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-7

Difference of Two Cubes

a3 – b3 = (a – b) (a2 + ab + b2)

Example:a.) Factor 27x3 – 8y6.

)469)(23(

])2()2)(3()3)[(23(

)2()3(827

4222

22222

32363

yxyxyx

yyxxyx

yxyx

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-8

Helpful Hint for Factoring

When factoring the sum or difference of two cubes, the sign between the terms in the binomial factor will be the same as the sign between the terms.

The sign of the ab term will be the opposite of the sign between the terms of the binomial factor.

a3 + b3 = (a + b) (a2 – ab + b2)

same sign

The last term in the trinomial will always be positive.

a3 – b3 = (a – b) (a2 + ab + b2)same sign

opposite sign always positive

opposite sign always positive