Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 5 - Section 5.6 - Factoring Trinomials - Exercise Set: 54

Answer

$2x^3(5x+1)(2x+5)$

Work Step by Step

Factoring the $GCF=2x^3$, then the given expression, $ 20x^5+54x^4+10x^3 $, is equivalent to $ 2x^3(10x^2+27x+5) $.\\ The two numbers whose product is $ac= 10(5)=50 $ and whose sum is $b= 27 $ are $\{ 2,25 \}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $ 2x^3(10x^2+27x+5) $, is \begin{array}{l}\require{cancel} 2x^3(10x^2+2x+25x+5) \\\\= 2x^3[(10x^2+2x)+(25x+5)] \\\\= 2x^3[2x(5x+1)+5(5x+1)] \\\\= 2x^3[(5x+1)(2x+5)] \\\\= 2x^3(5x+1)(2x+5) .\end{array}
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