I went through my completed pretest with a classmate and came across this problem:

Factor x^4-4x^2-45 into linear factors allowing complex numbers. If you use your graphing calculator, be sure to explain your reasoning. No decimals.

Here's what I did. I determined that (x+3)(x-3) are zeros of the function. So I divided x^4-4x^2-45 by x^2-9.

I got x^2+5, which I factored out into (x+2i(square root 1))(x-2i(square root 1)), then my final answer was:

(x-3)(x+3)(x+2i(square root 1))(x-2i(square root 1))

Assuming that I simplified this correctly, it should be right. Right? My classmate had (x-3)(x+3)(x+i(square root 5))(x+i(square root 5)).

I'm not sure about it because my teacher hasn't put up a key for this. Did I do this correctly? Thanks in advance.