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.

Re: Linear factors with complex numbers.

Quote:

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.

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

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.

Re: Linear factors with complex numbers.

Quote:

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.

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.

Re: Linear factors with complex numbers.

Quote:

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.

Re: Linear factors with complex numbers.