Question 1172003
if 4+i is a root, then 4-i is a root, since complex roots are conjugate.
two of the factors are (x+2) and x
The other two are from (x-4-i) and (x-4+i)
If we multiply those factors together, we get 
x^2-4x+ix-4x+16+4i-ix+4i-i^2=x^2-8x+17

The factors are x, (x+2), and x^2-8x+17. 
f(x) is their product, or x(x+2)(x^2-8x+17)