Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 5 - Review Exercises - Page 360: 5


$(x+3) \left( x-3 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ (x+3)(4x-1)-(x+3)(3x+2) ,$ get the $GCF.$ Then, divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient. $\bf{\text{Solution Details:}}$ Factoring the $GCF= x+3 ,$ the expression above is equivalent to \begin{array}{l}\require{cancel} (x+3) \left( \dfrac{(x+3)(4x-1)}{x+3}-\dfrac{(x+3)(3x+2)}{x+3} \right) \\\\= (x+3) \left( (4x-1)-(3x+2) \right) \\\\= (x+3) \left( 4x-1-3x-2 \right) \\\\= (x+3) \left( x-3 \right) .\end{array}
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