Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set: 74

Answer

$2t^2(s^3+2t)(s^3+3t)$

Work Step by Step

Factoring the $GCF= 2t^2 $, then the given expression, $ 2s^6t^2+10s^3t^3+12t^4 $ is equivalent to \begin{array}{l} 2t^2(s^6+5s^3t+6t^2) .\end{array} The two numbers whose product is $ac= 1(6)=6 $ and whose sum is $b= 5 $ are $\{ 2,3 \}$. Using these two numbers to decompose the middle term of the expression, $ 2t^2(s^6+5s^3t+6t^2) ,$ then the factored form is \begin{array}{l} 2t^2(s^6+2s^3t+3s^3t+6t^2) \\\\= 2t^2[(s^6+2s^3t)+(3s^3t+6t^2)] \\\\= 2t^2[s^3(s^3+2t)+3t(s^3+2t)] \\\\= 2t^2[(s^3+2t)(s^3+3t)] \\\\= 2t^2(s^3+2t)(s^3+3t) .\end{array}
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