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

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

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:**1731**Joined:**Mon Dec 08, 2008 4:22 pm-
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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?

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:**305**Joined:**Mon Dec 08, 2008 12:32 am-
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gradam wrote:...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!!