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 - 3.5 Special Factoring Techniques - 3.5 Exercises - Page 279: 39


$2\left( 4x^8+6x^4+9 \right)$

Work Step by Step

$\bf{\text{Solution Outline:}}$ Get the $GCF$ of the given expression, $ 8x^8+12x^4+18 .$ 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 $\{ 8,12,18 \}$ is $ 2 $ since it is the highest number that can divide all the given constants. Factoring the $GCF= 2 ,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2\left( \dfrac{8x^8}{2}+\dfrac{12x^4}{2}+\dfrac{18}{2} \right) \\\\= 2\left( 4x^8+6x^4+9 \right) .\end{array}
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