Find an nth-degree polynomial function

Question

N=3

4 and 2i are zeros

f(1)= -15

Answer 1

x=4

x-4=0 is a factor

x=2i

x^2=-4

x+4 is another factor

multiply the factors with an unknown constant "a"

f(x) = a(x-4)(x^2 + 4)

f(1)=-15 = a(-3)(5)

a= -15/-15 = 1

f(x)= x^3 -4x^2 +4x =16

n=3

or for n>3

just put in some integer exponents on each factor, m and p

f(x)= a(x-4)^m(x^2+4)^p

where m+2^p=n>3

and recalculate a