Answer
$ x=-2,-1$ and $x=1$ (multiplicity 2).
$f(x)=(x+2)(x+1)(x-1)^2$
Work Step by Step
Step 1. For $f(x)=x^4+x^3-3x^2-x+2$, list possible rational real zeros $\frac{p}{q}: \pm1,\pm2$
Step 2. Use synthetic division to find one zero as shown in the figure to find a zeros $x=\pm1$.
Step 3. Use the quotient to find other zeros: $x^2+x-2=0\Longrightarrow (x+2)(x-1)=0 \Longrightarrow x=-2,1$.
Step 4. Factor the polynomial $f(x)=(x+2)(x+1)(x-1)^2$
