Form a Polynomial f(x)

Question

Degree: 4, Zeros: 2+2i;-5, Multiplicity:2
f(x)=a(______________)

Answer 1

interpretation:
4 roots:
2+2i
2-2i
-5
-5

the -5 root twice yields (x+5)^2
for the two complex roots:
sum of those two = 4
product of those two = (2+2i)(2-2i) = 8
which gives us the trinomial x^2 -4x + 8

so f(x) = a(x^2 - 4x + 8)(x+5)^2 , where a is any non-zero constant

Answer 2

10