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 – 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 a 2 – b 2 = (a + b) (a – b) Example: a.) Factor x 2 – 16. x 2 – 16 = x 2 – 4 2 = (x + 4)(x – 4) b.) Factor 25x 2 – 36y 2. 25x 2 – 36y 2 = (5x) 2 – (6y) 2 = (5x + 6y)(5x – 6y)

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-5 Factor Perfect Square Trinomials a 2 + 2ab + b 2 = (a + b) 2 a 2 – 2ab + b 2 = (a – b) 2 Example: a.) Factor x 2 – 8x 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) = 8x x 2 – 8x + 16 = (x – 4) 2

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-6 Sum of Two Cubes a 3 + b 3 = (a + b) (a 2 – ab + b 2 ) Example: a.) Factor the sum of cubes x

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-7 Difference of Two Cubes a 3 – b 3 = (a – b) (a 2 + ab + b 2 ) Example: a.) Factor 27x 3 – 8y 6.

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. a 3 + b 3 = (a + b) (a 2 – ab + b 2 ) same sign The last term in the trinomial will always be positive. a 3 – b 3 = (a – b) (a 2 + ab + b 2 ) same sign opposite sign always positive opposite sign always positive