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.
In my original post I had worked it out already, and I wanted to know if I had done it correctly.
x^2-4x^2-45=(x^2-9)(x^2+5)
I came up with:
(x-3)(x+3)(x+2i(square root 1))(x-2i(square root 1))
While my classmate left it at:
(x-3)(x+3)(x+i(square root 5))(x-i(square root 5))
I want to know if this is correct.