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: 50

Answer

$2(x-3)(x-4)$

Work Step by Step

Factoring the $GCF= 2 ,$ the given expression, $ 2x^2-14x+24 ,$ is equivalent to \begin{array}{l}\require{cancel} 2(x^2-7x+12) .\end{array} The trinomial expression above has $c= 12 $ and $b= -7 .$ The possible factors of $c$ are $ \{ 1,12 \} ,\{ 2,6 \} ,\{ 3,4 \} ,\{ -1,-12 \} ,\{ -2,-6 \} ,\{ -3,-4 \} $. Among these factors, the pair whose sum is equal to $b$ is $\{ -3,-4 \}.$ Hence, the factored form of the given expression is \begin{array}{l}\require{cancel} 2(x-3)(x-4) .\end{array}
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