## How does x^4+x^2+1 = (x^2+x+1)(x^2+x+1)?

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
Posts: 2
Joined: Thu Aug 29, 2013 3:29 pm
Contact:

### How does x^4+x^2+1 = (x^2+x+1)(x^2+x+1)?

Hi!

I'm trying to solve that how does x^4+x^2+1 become (x^2+x+1)(x^2+x+1).
Can someone help me?

I know the goal, but cant figure out how to get there

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
I'm trying to solve that how does x^4+x^2+1 become (x^2+x+1)(x^2+x+1).
Are you saying that you need to figure out how to do the factorization, or that you need to confirm that the factorization is correct, or something else? Thank you!

Posts: 2
Joined: Thu Aug 29, 2013 3:29 pm
Contact:

### Re: How does x^4+x^2+1 = (x^2+x+1)(x^2+x+1)?

Thank you for the fast reply

This was an exercise from my math workbook about factorization. After a lot of tries I gave up and checked the answer, but I still couldn't figure out how to do the factorization. What's the method of that?

maggiemagnet
Posts: 358
Joined: Mon Dec 08, 2008 12:32 am
Contact:

### Re: How does x^4+x^2+1 = (x^2+x+1)(x^2+x+1)?

...how does x^4+x^2+1 become (x^2+x+1)(x^2+x+1).

This was an exercise from my math workbook about factorization. After a lot of tries I gave up and checked the answer, but I still couldn't figure out how to do the factorization. What's the method of that?
I don't know. This doesn't have any x-intercepts, so you can't find zeroes and then go backwards from that. It's a square, for sure, but I'm not seeing how you're supposed to "see" that in the first place. I did find a trick online, though; maybe you're supposed to "know" this??

x^4 + x^2 + 1
x^4 + 1 + x^2
x^4 + 1 + x^2 + 2x^2 - 2x^2 <== [this is the "trick"!]
x^4 + 2x^2 + 1 + x^2 - 2x^2
(x^2 + 1)^2 - x^2
(x^2 + 1)^2 - (x)^2

Then do difference of squares:

[(x^2 + 1) + (x)][(x^2 + 1) - (x)]
[x^2 + 1 + x][x^2 + 1 - x]
[x^2 + x + 1][x^2 - x + 1]

By the way, this solution shows that the "answer" they gave you in the back is wrong!!