Intermediate Algebra (12th Edition)

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

Chapter 5 - Section 5.1 - Greatest Common Factors and Factoring by Grouping - 5.1 Exercises: 43


$-12s^4 \left( s-4 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ First, get the $GCF$ of the given expression, $ -12s^5+48s^4 .$ Then, divide the given expression and the $GCF.$ Express the answer as the product of the $GCF$ and the resulting quotient. Finally, factor out the $-1$. $\bf{\text{Solution Details:}}$ The $GCF$ of the constants of the terms $\{ -12,48 \}$ is $ 12 .$ The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{ s^5,s^4 \}$ is $ s^4 .$ Hence, the entire expression has $GCF= 12s^4 .$ Factoring the $GCF= 12s^4 ,$ the given expression is equivalent to \begin{array}{l}\require{cancel} 12s^4 \left( \dfrac{-12s^5}{12s^4}+\dfrac{48s^4}{{12s^4}} \right) .\end{array} Using the Quotient Rule of the laws of exponents which states that $\dfrac{x^m}{x^n}=x^{m-n},$ the expression above simplifies to \begin{array}{l}\require{cancel} 12s^4 \left( -s^{5-4}+4s^{4-4} \right) \\\\= 12s^4 \left( -s^{1}+4s^{0} \right) \\\\= 12s^4 \left( -s+4(1) \right) \\\\= 12s^4 \left( -s+4 \right) .\end{array} Factoring out $-1$ from the second factor results to \begin{array}{l}\require{cancel} -12s^4 \left( s-4 \right) .\end{array}
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