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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.

  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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Another means of solutionMike C2007-03-22 14:32:29
solutionxdog2007-03-22 09:53:51
SolutionAn Attempt To The SolutionK Sengupta2007-03-22 00:42:24
QuestionHow's this? (Probable spoiler)Jer2007-03-21 11:07:37
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