Answer
$\{2, \pm \sqrt 5 \}$, $f(x)=2(x-2)(x+\sqrt 5)(x-\sqrt 5)$
Work Step by Step
Step 1. Given $f(x)=2x^3-4x^2-10x+20$, list possible rational zeros as $\frac{p}{q}=\pm1,\pm2,\pm4,\pm5,\pm10,\pm20,\pm\frac{1}{2},\pm\frac{5}{2}$
Step 2. Use synthetic division as shown in the figure to find one zero $x=2$.
Step 3. Use the quotient to solve $2x^2-10=0$ or $x^2=5$, thus $x=\pm \sqrt 5$
Step 4. Thus the real zeros are $\{2, \pm \sqrt 5 \}$ and we can factor the function as $f(x)=2(x-2)(x+\sqrt 5)(x-\sqrt 5)$