Elementary Algebra

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

Chapter 6 - Factoring, Solving Equations, and Problem Solving - Chapter 6 Review Problem Set: 12

Answer

$(x+1)(4x-7)$

Work Step by Step

In accordance with the rules of factoring trinomials, we need to find two integers whose product is $-28$ and whose sum is $-3$. A little searching determines that these numbers are $4$ and $-7$. Therefore, we can express the middle term $-3x$ as $(4x-7x)$ and proceed to factoring by grouping: $4x^{2}-3x-7$ =$4x^{2}+4x-7x-7$ =$4x(x+1)-7(x+1)$ =$(x+1)(4x-7)$
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