Find the nth degree polynomial

Question

n=3

-3 and 7+5i are zeros

f(-1) = 178

Answer 1

There are three factors that combine to create the 3rd level polynomial. The fact that one factor is a complex number implies that its complement is also a factor. Hence the desired polynomial is the product of the three factors that create the roots:

F(x) = (x+3)(x-7+5i)(x-7-5i)

F(x) = x^3 -11x^2 +3x +222