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 Basic Factoring (Posted on 2007-03-21)
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.

 Submitted by Brian Smith Rating: 3.0000 (1 votes) Solution: (Hide) Start with: x^6-1 = x^6-1 Apply (1) to the left side and (2) to the right side: (x^3-1)(x^3+1) = (x^2-1)(x^4+x^2+1) Next, apply (2) and (3) to the respective factors on the left side and apply (1) to (x^2-1) on the right side (x-1)(x^2+x+1)(x+1)(x^2-x+1) = (x-1)(x+1)(x^4+x^2+1) Since (x-1)(x+1) appears on each side, the factorization of x^4+x^2+1 is (x^2+x+1)(x^2-x+1) Check the comments for more ways to solve the problem, some of which include other equally basic factoring identites and methods.

 Subject Author Date Another means of solution Mike C 2007-03-22 14:32:29 solution xdog 2007-03-22 09:53:51 An Attempt To The Solution K Sengupta 2007-03-22 00:42:24 How's this? (Probable spoiler) Jer 2007-03-21 11:07:37

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