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 - Page 261: 8



Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two integers whose product is $56$ and whose sum is $-30$. A little searching determines that these numbers are $-2$ and $-28$. Therefore, we can express the middle term $-30x$ as $(-2x-28x)$ and proceed to factoring by grouping: $8x^{2}-30x+7$ =$8x^{2}-2x-28x+7$ =$2x(4x-1)-7(4x-1)$ =$(4x-1)(2x-7)$
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