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: 83

Answer

$z(z+6)(z^2-6)$

Work Step by Step

Factoring the $GCF= z $, then the given expression, $ z^4+6z^3-6z^2-36z $ is equivalent to \begin{array}{l} z(z^3+6z^2-6z-36) .\end{array} Using factoring by grouping, the factored form of the expression, $ z(z^3+6z^2-6z-36) ,$ \begin{array}{l} z[(z^3+6z^2)-(6z+36)] \\\\= z[z^2(z+6)-6(z+6)] \\\\= z[(z+6)(z^2-6)] \\\\= z(z+6)(z^2-6) .\end{array}
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