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: 37

Answer

$(7a-2)(3a+1)$

Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two variables whose product is $21(-2)=-42$ and whose sum is $1$. A little searching determines that these numbers are $-6$ and $7$. Therefore, we can express the middle term $a$ as $(-6a+7a)$ and proceed to factoring by grouping: $21a^{2}+a-2$ =$21a^{2}-6a+7a-2$ =$3a(7a-2)+1(7a-2)$ =$(7a-2)(3a+1)$
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