Answer
$-2,1,4$.
$f(x) =(x+2)(x-1)(x-4)$.
Work Step by Step
Step 1. List possible rational zeros $\frac{p}{q}:\pm1,\pm2,\pm4,\pm8$.
Step 2. Use synthetic division as shown to find zero(s) $x=1$.
Step 3. Use the quotient to find other zero(s) $x^2-2x-8=0 \Longrightarrow (x+2)(x-4)=0 \Longrightarrow x=-2,4$.
Step 4. Thus $f(x)=x^3-3x^2-6x+8=(x+2)(x-1)(x-4)$.
