Chapter 5 - Polynomials and Factoring - 5.2 Factoring Trinomials of the Type x2+bx+c - 5.2 Exercise Set - Page 317: 35

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

Factoring the $GCF= x^3 $, the given expression, $ x^5-x^4-2x^3 ,$ is equivalent to \begin{array}{l} x^3(x^2-x-2) .\end{array} The 2 numbers whose product is $ac= 1(-2)=-2 $ and whose sum is $b= -1 $ are $\left\{ -2,1 \right\}.$ Using these two numbers to decompose the middle term of the above trinomial, then \begin{array}{l} x^3(x^2-2x+1x-2) \\\\= x^3[(x^2-2x)+(1x-2)] \\\\= x^3[x(x-2)+(x+2)] \\\\= x^3[(x-2)(x+1)] \\\\= x^3(x-2)(x+1) .\end{array}