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

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