1. 4-4 FACTORING QUADRATIC
EXPRESSIONS
Chapter 4 Quadratic Functions and Equations
©Tentinger

2. ESSENTIAL UNDERSTANDING AND
OBJECTIVES
 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

3. IOWA CORE CURRICULUM
 Algebra
 A.SSE.2. Use the structure of an expression to
identify ways to rewrite it.

4.  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.

5. DISTRIBUTIVE METHOD:
 (x + 4)(x + 2)

6. FOIL METHOD
 F: first; O: Outer; I: Inner; L: last
 (x + 4)(x + 2)

7. FACTORING
 To factor, think of FOIL in reverse
 Factor x2 + 6x + 8
 What factors of 8 add to be 6?
 Factoring ax2 + bx + c when a = ± 1
 x2 + 9x + 20
 x2 + 14x – 72
 - x2 + 13x – 12

8. MORE FACTORING
 x2 + 14x + 40
 x2 – 11x +30
 - x2 + 14x +32

9. 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 x2 + 9x
 4 x2 + 20x – 56
 7 n2 – 21

10. WHAT IS THE EXPRESSION IN FACTORED
FORM?
 9 n2 + 9n – 18
 4 x2 + 8x + 12

11. FACTORING AX2 + BX + C WHEN A ≠±1
AND THE GCF = 1
 Find factors of a times c (ac) that add to be b
 2x2 + 11x + 12
 4x2 – 4x – 3
 4x2 + 7x + 3
 2x2 – 7x + 6

12. PERFECT SQUARE TRINOMIAL
 A trinomial that is a square of a binomial
 Example: x2 + 10x + 25 = (x + 5)2
 Forms
 a2 + 2abx + b2 = (a + b)2
 a2 - 2abx + b2 = (a - b)2
 Factor the following
 1. 4x2 – 24x + 36
 2. 64x2– 16x + 1

13. DIFFERENCE OF TWO SQUARES
 a2 – b2 = (a + b)(a - b)
 Factor the following
 1. 25x2 – 49
 2. 16x2 – 81

14. HOMEWORK
 Pg. 221 – 222
 # 15 – 78 (3s)
 (22 problems)