Answer
$2,2,\pm i\sqrt 5$
$f(x)=(x^2+5)(x-2)^2$
Work Step by Step
Step 1. Based on the Rational Zeros Theorem, list possible rational zeros $\frac{p}{q}=\pm1,\pm2,\pm4,\pm5,\pm10,\pm20$
Step 2. Use synthetic division to find one or more zeros $x=2,2$ as shown in the figure.
Step 3. Use to the quotient to solve $x^2+5=0$ or $x^2=-5$, thus $x=\pm i\sqrt 5$
Step 4. We can factor the function as $f(x)=(x^2+5)(x-2)^2$
