Given that 2−2i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x^4+3x^3−10x^2+16x+80

Answer 1

If 2-2i is a root, then 2+2i must also be a root, since all your coefficients are real.

Multiplying these two roots together gives you x^2 - 4x + 8. Do long division to get that the other factor is x^2 + 7x + 10. Then factor it into (x+2)(x+5).

(x+2)(x+5) (x-(2+2i)) (x-(2-2i))