Intermediate Algebra (12th Edition)

Published by Pearson

Chapter 5 - Review Exercises - Page 360: 1

Answer

$6p \left( 2p-1 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $12p^2-6p ,$ get the $GCF.$ Then, divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient. $\bf{\text{Solution Details:}}$ The $GCF$ of the constants of the terms $\{ 12,-6 \}$ is $6$ 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 $\{ p^2,p \}$ is $p .$ Hence, the entire expression has $GCF= 6p .$ Factoring the $GCF= 6p ,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 6p \left( \dfrac{12p^2}{6p}-\dfrac{6p}{6p} \right) \\\\= 6p \left( 2p-1 \right) .\end{array}

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