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