Answer
$(x-1)(x+1)(x+2)$
Work Step by Step
Group the first two terms together and group the last two terms together.
$x^3+2x^2-x-2=(x^3+2x^2)+(-x-2)$
Factor out the GCF in each group.
$=x^2(x+2)+(-1)(x+2)$
$=x^2(x+2)-1(x+2)$
Factor out $(x+2)$.
$=(x+2)(x^2-1)$
$=(x+2)(x^2-1^2)$
Use the special formula $a^2-b^2=(a+b)(a-b)$ where $a=x$ and $b=1$.
$=(x+2)(x+1)(x-1)$
$=(x-1)(x+1)(x+2)$
Hence, the completely factored form of the given expression is $(x-1)(x+1)(x+2)$.
