Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 6 - Section 6.2 - Factoring Trinomials Whose Leading Coefficient is 1 - Exercise Set: 48

Answer

$2(x-3)(x+8)$

Work Step by Step

Factoring the $GCF= 2 ,$ the given expression, $ 2x^2+10x-48 ,$ is equivalent to \begin{array}{l}\require{cancel} 2(x^2+5x-24) .\end{array} The trinomial expression above has $c= -24 $ and $b= 5 .$ The possible factors of $c$ are $ \{ 1,-24 \} ,\{ 2,-12 \} ,\{ 3,-8 \} ,\{ 4,-6 \} ,\{ -1,24 \} ,\{ -2,12 \} ,\{ -3,8 \} ,\{ -4,6 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -3,8 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} 2(x-3)(x+8) .\end{array}
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