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: 5

Answer

$x^{2}$ - 5x -14 = (x+2)(x-7)

Work Step by Step

$x^{2}$ - 5x -14 = (x+2) (x__) step 1. Enter x as the first term of each factor $x^{2}$ - 5x -14 = (x+2) (x__) Step 2. To find the second term of each factor, we must find two integers whose product is -14 and whose sum is -5 List pairs of factors of the constant, -30 (1,-14)(-1,14)(-2,7),(2,-7) step 3. The correct factorization of $x^{2}$ - 5x -14 is the one in which the sum of the Outside and Inside products is equal to -5. So (2,-7) satisfy the condition $x^{2}$ - 5x -14 = $x^{2}$ + 2x -7x - 14 = (x+2)(x-7)
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