Question

Which of the following is a polynomial with roots -4, -2i, and 2i ?

Answer 1

You haven't provided any polynomials.

A polynomial with those roots will have the value 0 when evaluated at -4, -2i, and 2i.

If written in factored form, it will include product terms \((x+4)(x-2i)(x+2i)\)

Answer 2

a. x3 - 4x2 + 4x - 16
b. x3 + 4x2 + 4x + 16
c. x3 + 2x2 + 4x + 8
d. x3 - 2x2 + 4x - 8

Answer 3

Okay, the leading coefficient in each of those polynomials is 1 (\(x^3=1x^3)\) so you could also make your selection by multiplying together the factors that I gave you and see which polynomial matches:
\[(x+4)(x-2i)(x+2i)=\]If you go that route, I suggest you multiply the \((x-2i)(x+2i)\) terms first