Chapter 5 - Polynomials and Factoring - 5.6 Factoring: A General Strategy - 5.6 Exercise Set - Page 344: 83

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

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}