Answer
$x^6-6x^5+21x^4-64x^3-65x^2-58x-85$
Work Step by Step
Step 1. Given zeros $x=-1,5, -i, 1+4i$, we can identify two more zeros as $x=i, 1-4i$
Step 2. We can write the polynomial as $f(x)=(x+1)(x-5)(x+i)(x-i)(x-1-4i)(x-1+4i)=(x^2-4x-5)(x^2+1)((x-1)^2-(4i)^2)=(x^2-4x-5)(x^2+1)(x^2-2x+17)$
Step 3. Continue from above, we have $f(x)=(x^2+1)(x^4+(-2-4)x^3+(17-5+8)x^2+(10-68)x-85)=(x^2+1)(x^4-6x^3+20x^2-58x-85)=x^6-6x^5+21x^4-64x^3-65x^2-58x-85$
