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

2 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter – Factoring a Monomial from a Polynomial 5.2 – Factoring by Grouping 5.3 – Factoring Trinomials of the Form ax 2 + bx + c, a = – Factoring Trinomials of the Form ax 2 + bx + c, a ≠ – Special Factoring Formulas and a General Review of Factoring 5.6 – Solving Quadratic Equations Using Factoring 5.7 – Applications of Quadratic Equations Chapter Sections

3 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-3 Factoring Trinomials of the Form ax 2 + bx + c, a = 1

4 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-4 Factoring Trinomials Recall that factoring is the reverse process of multiplication. Using the FOIL method, we can show that (x + 3)(x + 4) = x 2 + 7x x 2 + 7x + 12 = (x + 3)(x + 4) Therefore x 2 + 7x + 12 = (x + 3)(x + 4) Note that this trinomial results in the product of two binomials whose first term is x and second term is a number (including its sign).

5 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-5 Factoring Trinomials Factoring any polynomial of the form x 2 + bx + c will result in a pair of binomials: Numbers go here. x 2 + bx + c = (x +?)(x +?) O ( x + 3 )( x + 4 ) F I L = x 2 + 4x + 3x + 12 = x 2 + 7x + 12 FOIL

6 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-6 Factoring Trinomials 1.Find two numbers whose product equals the constant, c, and whose sum equals the coefficient of the x-term, b. 2.Use the two numbers found in step 1, including their signs, to write the trinomial in factored form. The trinomial in factored form will be (x + first number) (x + second number)

7 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-7 Examples a.) Factor x x x x - 60 = (x + ?) (x + ?) Replace the ?s with two numbers that are the product of -60 and the sum of -11. x 2 + 8x + 15 = (x -15) (x + 4) b.) Factor x 2 + 5x This is a prime polynomial because it cannot be factored.

8 Copyright © 2015, 2011, 2007 Pearson Education, Inc. Chapter 5-8 Examples Continued c.) Factor x 2 + 3xy + 2y 2. We must find two numbers whose product is 2 (from 2y2) and whose sum is 3 (from 3xy). The two numbers and 1 and 2. Thus, x 2 + 3xy + 2y 2 = (x + 1y)(x + 2y) = (x + y)(x + 2y)