Answer
$\{-5,-4,1 \}$, $f(x)=(x+5)(x+4)(x-1)$
Work Step by Step
Step 1. Given $f(x)=x^3+8x^2+11x-20$, list possible rational zeros as $\frac{p}{q}=\pm1,\pm2,\pm4,\pm5,\pm10,\pm20$
Step 2. Use synthetic division as shown in the figure to find one zero $x=1$.
Step 3. Use the quotient to solve $x^2+9x+20=0$ or $(x+5)(x+4)=0$, thus $x=-5,-4$
Step 4. Thus the zeros are $\{-5,-4,1 \}$ and we can factor the function as $f(x)=(x+5)(x+4)(x-1)$
