Answer
$2x^4-2x^3-2x^2-2x-4$
Work Step by Step
Step 1. Since $i$ is a zero, $-i$ is also a zero.
Step 2. Use the other zeros, we can write the polynomial as $f(x)=k(x+1)(x-2)(x-i)(x+i)=k(x+1)(x-2)(x^2+1)$ where $k$ is a constant.
Step 3. Use $f(3)=80$, we have $k(4)(1)(10)=80$ which gives $k=2$.
Step 4. Thus $f(x)=2(x+1)(x-2)(x^2+1)=2x^4-2x^3-2x^2-2x-4$
