Polynomials and Polynomial Functions Chapter 5 Polynomials and Polynomial Functions

Chapter Sections 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 1 Outline

Special Factoring Formulas § 5.6 Special Factoring Formulas

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)

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) = 8x x2 – 8x + 16 = (x – 4)2

Sum of Two Cubes a3 + b3 = (a + b) (a2 – ab + b2) Example: a.) Factor the sum of cubes x3 + 64.

Difference of Two Cubes a3 – b3 = (a – b) (a2 + ab + b2) Example: a.) Factor 27x3 – 8y6.

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. The last term in the trinomial will always be positive. a3 + b3 = (a + b) (a2 – ab + b2) same sign opposite sign always positive a3 – b3 = (a – b) (a2 + ab + b2) same sign opposite sign always positive