Answer
$-2,1,4$
$f(x)=(x+2)(x-1)(x-4)$
Work Step by Step
Step 1. Based on the Rational Zeros Theorem, list possible rational zeros $\frac{p}{q}=\pm1,\pm2,\pm4,\pm8$
Step 2. Use synthetic division to find one or more zeros $x=1$ as shown in the figure.
Step 3. Use to the quotient to solve $x^2-2x-8=0$ or $(x+2)(x-4)=0$, thus $x=-2,4$
Step 4. We can factor the function as $f(x)=(x+2)(x-1)(x-4)$
