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 - Concept and Vocabulary Check - Page 399: 4



Work Step by Step

$x^{2}$ - x -30 = (x- 6)(x__) step 1. Enter x as the first term of each factor $x^{2}$ - x -30 = (x- 6)(x__) Step 2. To find the second term of each factor, we must find two integers whose product is 18 and whose sum is -1 List pairs of factors of the constant, -30 (1,-30)(-1,30)(-2,15),(2,-15)(-3,10)(3,-10)(5,-6)(-5,6) step 3. The correct factorization of $x^{2}$ - x - 30is the one in which the sum of the Outside and Inside products is equal to -x. So (-6,5) satisfy the condition $x^{2}$ - x - 30= $x^{2}$ - 6x + 5x - 30 = (x-6)(x+5)
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