n=3; 2 and 2 i are zereos; f (-1)=30

Question

find the nth-degree polynomial function with real coefficients satisfying the given conditions

Answer 1

The polynomial has the form f(x)=a(x-2)(x+2i)(x-2i)=a(x-2)(x²+4)=a(x³-2x²+4x-8).

f(-1)=a(-1-2-4-8)=-15a=30, so a=-2.

f(x)=-2x³+4x²-8x+16.