Answer
$\{-3,-1,2 \}$, $f(x)=(x+3)(x+1)(x-2)$
Work Step by Step
Step 1. Given $f(x)=x^3+2x^2-5x-6$, list possible rational zeros as $\frac{p}{q}=\pm1,\pm2,\pm3$
Step 2. Use synthetic division as shown in the figure to find one zero $x=2$.
Step 3. Use the quotient $x^2+4x+3=0$ or $(x+3)(x+1)=0$, thus $x=-3,-1$
Step 4. Thus the zeros are $\{-3,-1,2 \}$ and we can factor the function as $f(x)=(x+3)(x+1)(x-2)$
