When math students are taught factoring, usually the first thing they learn are special factoring identities such as:

1: a²-b²= (a-b)(a+b)
2: a³-b³ = (a-b)(a²+ab+b²)
3: a³+b³ = (a+b)(a²-ab+b²)

Find a factorization of the expression x⁴+x²+1 using only those identities.

(In reply to An Attempt To The Solution by K Sengupta)

x^4 + x^2 + 1 =

x^4 + 2x^2 + 1 - x^2 =

(x^2 + 1)^2 - x^2 =

(x^2 + 1 + x) (x^2 + x - 1)

Sorry for the cruddy editing.

Edited on March 22, 2007, 9:54 am

Posted by xdog on 2007-03-22 09:53:51