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Basic Factoring (Posted on 2007-03-21) Difficulty: 2 of 5
When math students are taught factoring, usually the first thing they learn are special factoring identities such as:

1: a-b= (a-b)(a+b)
2: a-b = (a-b)(a+ab+b)
3: a+b = (a+b)(a-ab+b)

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

See The Solution Submitted by Brian Smith    
Rating: 3.0000 (1 votes)

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Question How's this? (Probable spoiler) | Comment 1 of 4

x^4 + x + 1
x^4 - x + 2x + x - x + 1  [add zero as -x + x + x - x]
(x + x)(x - x) + x + x + x - x + 1  [rule 1]
(x + x)(x - x) + (x + x) + (x - x + 1) [group terms]
(x + x)(x - x + 1) + (x - x + 1) [monomial factor] 
(x + x +1)(x - x + 1) [monomial factor]

I assume this is ok as the factoring either involves rule 1 or does not involve an identity.


  Posted by Jer on 2007-03-21 11:07:37
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