Answer
$x^4+2x^3-10x^2-6x+45$
Work Step by Step
Step 1. Given zeros $x=2+i$ and $x=-3$ (multiplicity 2), we can identify one more zeros as $x=2-i$
Step 2. We can write the polynomial as $f(x)=(x+3)^2(x-2-i)(x-2+i)=(x^2+6x+9)((x-2)^2-(i)^2)=(x^2+6x+9)(x^2-4x+5)$
Step 3. Continue from above, we have $f(x)=x^4+2x^3-10x^2-6x+45$
