Factoring x^3 + 1: how do they get (x + 1)(x^2 - x + 1)?

DarkLightA

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It sais x^3+1 can be factored to (x+1)(x^2-x+1). I don't get how you work this out though!?
 
Re: Factoring x^3+1?

DarkLightA said:
It sais x^3+1 can be factored to (x+1)(x^2-x+1). I don't get how you work this out though!?

There is a standard formula:

\(\displaystyle a^3 \, + \, b^3 \, = \, (a \, + \, b)\cdot (a^2 \, - \, a\cdot b \, + \, b^2)\)

edit: fixed the sign problem - thanks wjm
 
Re: Factoring x^3+1?

Check it out.

Does (x+1)(x[sup:1xbv1pl4]2[/sup:1xbv1pl4]-x+1) = x[sup:1xbv1pl4]3[/sup:1xbv1pl4]+1?
 
Re: Factoring x^3+1?

BTW, you should commit this to memory, as well as x^3 - 1 = (x - 1)(x^2 + x + 1)
 
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