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: 61

Answer

$2w^2(w+3)(w-16)$

Work Step by Step

Factoring the $GCF= 2w^2 ,$ the given expression, $ 2w^4-26w^3-96w^2 ,$ is equivalent to \begin{array}{l}\require{cancel} 2w^2(w^2-13w-48) .\end{array} The trinomial expression above has $c= -48 $ and $b= -13 .$ The possible factors of $c$ are $ \{ 1,-48 \} ,\{ 2,-24 \} ,\{ 3,-16 \} ,\{ 4,-12 \} ,\{ 6,-8 \} ,\{ -1,48 \} ,\{ -2,24 \} ,\{ -3,16 \} ,\{ -4,12 \} ,\{ -6,8 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ 3,-16 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} 2w^2(w+3)(w-16) .\end{array}
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