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: 14

Answer

(x-5)(x-9)

Work Step by Step

$x^{2}$ - 14x + 45 step 1. Enter x as the first term of each factor $x^{2}$ - 14x + 45 = (x__)(x _) Step 2. To find the second term of each factor, we must find two integers whose product is 45 and whose sum is -14 List pairs of factors of the constant, 45 (1,45)(-1,-45)(-3,-15)(3,15)(-5,-9)(5,9) step 3. The correct factorization of $x^{2}$ - 14x + 45 is the one in which the sum of the Outside and Inside products is equal to -14x. So (-5,-9) satisfy the condition $x^{2}$ -14x + 45 = $x^{2}$ -5x -9x + 45 = (x-5)(x-9)
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