Answer
$\frac{1}{2}$ (multiplicity 2), $-2$.
$f(x) =(2x-1)^2(x+2)$.
Work Step by Step
Step 1. List possible rational zeros $\frac{p}{q}:\pm1,\pm2,\pm\frac{1}{2},\pm\frac{1}{4}$.
Step 2. Use synthetic division as shown to find zero(s) $x=-2$.
Step 3. Use the quotient to find other zero(s) $4x^2-4x+1=0 \Longrightarrow (2x-1)^2=0 \Longrightarrow x=\frac{1}{2}$ (multiplicity 2).
Step 4. Thus $f(x)=4x^3+4x^2-7x+2=(2x-1)^2(x+2)$.
