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: 15

Answer

(x+3)(x-12)

Work Step by Step

$x^{2}$ - 9x -36 step 1. Enter x as the first term of each factor $x^{2}$ - 9x - 36= (x__)(x _) Step 2. To find the second term of each factor, we must find two integers whose product is -36 and whose sum is -9 List pairs of factors of the constant, -36 (1,-36)(-1,36)(-2,18)(2,-18)(3,-12)(-3,12)(4,-9)(-4,9)(6,-6) step 3. The correct factorization of $x^{2}$ - 9x - 36 is the one in which the sum of the Outside and Inside products is equal to -9x. So (3,-12) satisfy the condition $x^{2}$ -9x -36 = $x^{2}$ +3x -12x - 36= (x+3)(x-12)
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