5-4 F ACTORING QUADRATIC E XPRESSIONS Chapter 5 Quadratic Functions and Equations ©Tentinger

E SSENTIAL U NDERSTANDING AND O BJECTIVES Essential Understanding: you can factor many quadratic trinomials into products of two binomials Objectives : Students will be able to: Find common and binomial factors of quadratic expressions Factor special quadratics Perfect square trinomial Difference of two squares

I OWA C ORE CURRICULUM Algebra A.SSE.2. Use the structure of an expression to identify ways to rewrite it.

What are factors? What are the factors of 12? Factors of an expression are expressions that have a product equal to the given expression Factoring : rewriting an expression as a product of its factors You can use the Distributive Property or the FOIL method to multiply two binomials.

D ISTRIBUTIVE M ETHOD : (x + 4)(x + 2)

FOIL M ETHOD F: first; O: Outer; I: Inner; L: last (x + 4)(x + 2)

F ACTORING To factor, think of FOIL in reverse Factor x 2 + 6x + 8 What factors of 8 add to be 6? Factoring ax 2 + bx + c when a = ± 1 x 2 + 9x + 20 x x – 72 - x x – 12

M ORE FACTORING x x + 40 x 2 – 11x x x +32

GCF Greatest Common Factor (GCF) of an expression A common factor of the terms in the expression. Common factor with the great coefficient and the greatest exponent Finding Common Factors What is the expression in factored form? 6 x 2 + 9x 4 x x – 56 7 n 2 – 21

W HAT IS THE EXPRESSION IN FACTORED FORM ? 9 n 2 + 9n – 18 4 x 2 + 8x + 12

F ACTORING AX 2 + BX + C WHEN A ≠ ± 1 AND THE GCF = 1 Find factors of a times c (ac) that add to be b 2x x x 2 – 4x – 3 4x 2 + 7x + 3 2x 2 – 7x + 6

P ERFECT S QUARE T RINOMIAL A trinomial that is a square of a binomial Example: x x + 25 = (x + 5) 2 Forms a 2 + 2abx + b 2 = (a + b) 2 a 2 - 2abx + b 2 = (a - b) 2 Factor the following 1. 4x 2 – 24x x 2 – 16x + 1

D IFFERENCE OF T WO S QUARES a 2 – b 2 = (a + b)(a - b) Factor the following 1. 25x 2 – x 2 – 81