Factoring question

**dontoo** · March 26th 2010, 02:12 AM

Hi, I am factoring somewhat complex polynomials. For example this one:
$ a^3+b^3+c^3-3abc = $
$ = a^3+b^3+c^3-3abc-3a^2b+3^2b-3ab^2+3ab^2 = (a+b+b)(a^2+b^2+c^2-ab-ac-bc ) $
I only know to solve this kind of problems by guessing ( try to expand polynomial ). Is there a way to solve it by applying some algorithm?
Also link to some material that explains this topic would be great.

**sa-ri-ga-ma** · March 26th 2010, 03:36 AM

Hi dontoo, welcome to MHF.
$a^3 + b^3 + c^3 -3abc = (a+b)^3 + c^3 -3abc-3ab^2 - 3a^2b$
$= [(a+b+c)[(a+b)^2 + c^2 -(a+b)c] - 3ab(a+b+c)$
$= (a+b+c)[a^2 + b^2 +2ab -ac - bc -3ab]$
$= (a+b+c)(a^2+b^2+c^2-ab-bc-ac)$

**dontoo** · March 26th 2010, 05:42 AM

Thx for your replay. Is there is the way to solve it using polynomial zeros ( roots )?I don't want to guess how to expand polynomial.

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