Thinking Mathematically (6th Edition)

Published by Pearson
ISBN 10: 0321867327
ISBN 13: 978-0-32186-732-2

Chapter 6 - Algebra: Equations and Inequalities - 6.5 Quadratic Equations - Exercise Set 6.5: 9

Answer

(x+2)(x+3)

Work Step by Step

$x^{2}$ + 5x + 6 step 1. Enter x as the first term of each factor $x^{2}$ + 5x + 6 = (x+__)(x+__) Step 2. To find the second term of each factor, we must find two integers whose product is 6 and whose sum is 5 List pairs of factors of the constant, 6 (1,6)(2,3) step 3. The correct factorization of $x^{2}$ + 5x + 6 is the one in which the sum of the Outside and Inside products is equal to 5x. So (2,3) satisfy the condition $x^{2}$ + 5x + 6 = $x^{2}$ +2x+3x + 6 = (x+2)(x+3)
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