Answer
$f(x)=2x^4-4x^3+10x^2-68x+60$
Work Step by Step
Step 1. Given $x=3,1, -1+3i$ as zeros, we can identify an additional zero as $x=-1-3i$.
Step 2. We can write the polynomial as $f(x)=k(x-3)(x-1)(x+1-3i)(x+1+3i)=k(x^2-4x+3)(x^2+2x+10)=k(x^4-2x^3+5x^2-34x+30)$ where $k$ is an unknown constant.
Step 3. Use the condition $f(2)=-36$, we have $k(2^4-2(2)^3+5(2)^2-34(2)+30)=-36$, thus $k=2$
Step 4. Thus we have $f(x)=2x^4-4x^3+10x^2-68x+60$
