Intermediate Algebra (12th Edition)

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

Chapter 5 - Chapter 5 Test: 1

Answer

$11z \left( z-4\right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Get the $GCF$ of the given expression, $ 11z^2-44z .$ 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 $\{ 11,-44 \}$ is $ 11 $ 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 $\{ z^2,z \}$ is $ z .$ Hence, the entire expression has $GCF= 11z .$ Factoring the $GCF= 11z ,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 11z \left( \dfrac{11z^2}{11z}-\dfrac{44z }{11z}\right) \\\\= 11z \left( z-4\right) .\end{array}
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