Polynomial Degree 4; zeros:1, Multiplicity 2; 4i

Answer 1

The factor that gives a zero of 1 is (x-1) There are 2 of them, since it is multiplicity of 2. For 4i, complex zeros come in pairs. So you have to have (x-4i)(x+4i) as the factors.

f(x)=(x-4i)(x+4i)(x-1)(x-1) Now need to multiply everything together. I will FOIL the first 2 and last 2 terms.

(x²+4i-4i+16)(x²-x-x+1) Simplify

(x²+16)(x²-2x+1) Multiply

x⁴-2x³+x²+16x²-32x+16 Combine like terms

f(x)=x⁴-2x³+17x²-32x+16