find an nth degree

Question

Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value.

n=3
2 and 2i are zeros
f(-1)=-15

Answer 1

x = 2, x = 2i, x = -2i

f(x) = (x - 2)(x - 2i)(x + 2i)

f(x) = (x - 2)(x² - 4i²)

f(x) = (x - 2)(x² + 4)

f(x) = x³ - 2x² + 4x - 8

f(-1) = (-1)³ - 2(-1)² + 4(-1) - 8

f(-1) = -1 -2 - 4 - 8 = -15