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 280: 56



Work Step by Step

$\bf{\text{Solution Outline:}}$ To factor the given expression, $ 42x^2+24x+105xy+60y ,$ factor first the $GCF.$. Then group the terms such that the factored form of the groupings will result to a factor that is common to the entire expression. Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression. $\bf{\text{Solution Details:}}$ Factoring the $GCF=6,$ the given expression is equivalent to \begin{array}{l}\require{cancel} 3(14x^2+8x+35xy+20y) .\end{array} Grouping the first and third terms and the second and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} 3[(14x^2+35xy)+(8x+20y)] .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 3[7x(2x+5y)+4(2x+5y)] .\end{array} Factoring the $GCF= (2x+5y) $ of the entire expression above results to \begin{array}{l}\require{cancel} 3[(2x+5y)(7x+4)] \\\\= 3(2x+5y)(7x+4) .\end{array}
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