Question

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

A. x^3 – 4x^2 + 4x – 16

B. x^3 + 4x^2 + 4x + 16

C. x^3 + 2x^2 + 4x + 8

D. x^3 – 2x^2 + 4x – 8

Answer 1

your job is to multiply
\[(x+2)(x+2i)(x-2i)\]

Answer 2

second part is easy, because
\[(x+bi)(x-bi)=x^2+b^2\]

Answer 3

so your real job is to multiply
\[(x+2)(x^2+4)\] and see what you get

Answer 4

wait, how do you multiply x and -2i?

Answer 5

x^3 + 4x + 2x^2 + 8

x^3 + 2x^2 + 4x + 8

Answer 6

\[(x+2i)(x-2i)=x^2+2ix-2ix-2i\times 2i=x^2-4i^2=x^2+4\]

Answer 7

oh ok thanks!

Answer 8

yes you have it
yw