# Thread: Linear factors with complex numbers.

1. ## Linear factors with complex numbers.

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.

2. ## Re: Linear factors with complex numbers.

Originally Posted by FatimaA
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.

$\displaystyle x^4-4x^2-45=(x^2-9)(x^2+5)$

3. ## Re: Linear factors with complex numbers.

Hi,

I'm not sure this is the form he wants it in. I think my prof wants it to be totally factored out.

4. ## Re: Linear factors with complex numbers.

Originally Posted by FatimaA
Hi,

I'm not sure this is the form he wants it in. I think my prof wants it to be totally factored out.
Why do you think that is factored completely? Of course it is not.

You can now factor each of those two factors. We don't do your work for you.

5. ## Re: Linear factors with complex numbers.

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.

6. ## Re: Linear factors with complex numbers.

Originally Posted by FatimaA
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.
Yes that is correct.

You should learn to use symbols.

Type [TEX](x-i\sqrt{5})(x+i\sqrt{5}) [/TEX] gives $\displaystyle (x-i\sqrt{5})(x+i\sqrt{5})$
If you click on the “go advanced tab” you should see $\displaystyle \boxed{\Sigma}$ on the tool-bar. That gives the [TEX]..[/TEX] wrap. Your LaTeX code goes between them.

Thanks.