Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 3 - Exponents, Polynomials and Functions - 3.4 Factoring Polynomials - 3.4 Exercises - Page 271: 79


$4g \left( 3f+7 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Get the $GCF$ of the given expression, $ 12gf+28g .$ Divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient. $\bf{\text{Solution Details:}}$ The $GCF$ of the constants of the terms $\{ 12,28 \}$ is $ 4 $ since it is the highest number that can divide all the given constants. The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{ g,g \}$ is $ g .$ Hence, the entire expression has $GCF= 4g .$ Factoring the $GCF= 4g ,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 4g \left( \dfrac{12gf}{4g}+\dfrac{28g}{4g} \right) \\\\= 4g \left( 3f+7 \right) .\end{array}
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