Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.4 - Factoring Trinomials of the Form ax^2+bx+c - Problem Set 6.4: 20

Answer

$(3x-2)(3x+7)$

Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two variables whose product is $9(-14)=-126$ and whose sum is $15x$. A little searching determines that these numbers are $-6x$ and $21x$. Therefore, we can express the middle term $15x$ as $(-6x+21x)$ and proceed to factoring by grouping: $9x^{2}+15x-14$ =$9x^{2}-6x+21x-14$ =$3x(3x-2)+7(3x-2)$ =$(3x-2)(3x+7)$
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