Intermediate Algebra (12th Edition)

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

Chapter 5 - Review Exercises: 2

Answer

$7x \left( 3x+5 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ 21x^2+35x ,$ 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 $\{ 21,35 \}$ is $ 7 $ 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 $\{ x^2,x \}$ is $ x .$ Hence, the entire expression has $GCF= 7x .$ Factoring the $GCF= 7x ,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 7x \left( \dfrac{21x^2}{7x}+\dfrac{35x}{7x} \right) \\\\= 7x \left( 3x+5 \right) .\end{array}
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