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: 84

Answer

$t^2(t-2)(t^2+5)$

Work Step by Step

Factoring the $GCF= t^2 $, then the given expression, $ t^5-2t^4+5t^3-10t^2 $ is equivalent to \begin{array}{l} t^2(t^3-2t^2+5t-10) .\end{array} Using factoring by grouping, the factored form of the expression, $ t^2(t^3-2t^2+5t-10) ,$ \begin{array}{l} t^2[(t^3-2t^2)+(5t-10)] \\\\= t^2[t^2(t-2)+5(t-2)] \\\\= t^2[(t-2)(t^2+5)] \\\\= t^2(t-2)(t^2+5) .\end{array}
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