
Factoring question
Hi, I am factoring somewhat complex polynomials. For example this one:
$\displaystyle
a^3+b^3+c^33abc =
$
$\displaystyle
= a^3+b^3+c^33abc3a^2b+3^2b3ab^2+3ab^2
= (a+b+b)(a^2+b^2+c^2abacbc )
$
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.

Hi dontoo, welcome to MHF.
$\displaystyle a^3 + b^3 + c^3 3abc = (a+b)^3 + c^3 3abc3ab^2  3a^2b$
$\displaystyle = [(a+b+c)[(a+b)^2 + c^2 (a+b)c]  3ab(a+b+c) $
$\displaystyle = (a+b+c)[a^2 + b^2 +2ab ac  bc 3ab]$
$\displaystyle = (a+b+c)(a^2+b^2+c^2abbcac)$

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.