Answer
$x^4-2x^3-37x^2+38x+442$
Work Step by Step
Step 1. Given zeros $x=5+i, 4-i$, we can identify two more zeros as $x=5-i, 4+i$
Step 2. We can write the polynomial as $f(x)=(x-5-i)(x-5+i)(x-4+i)(x-4-i)=((x-5)^2-(i)^2)((x-4)^2-(i)^2)=(x^2-10x+25+1)(x^2+8x+16+1)=(x^2-10x+26)(x^2+8x+17)$
Step 3. Continue from above, we have $f(x)=x^4+(8-10)x^3+(17-80+26)x^2+(26(8)-170)x+26(17)=x^4-2x^3-37x^2+38x+442$
