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November 7th, 2009, 07:44 AM   #1
Joined: Nov 2009

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This is my first post .. i assume this is the correct place for my question
Is there any general way to factorize polynomials of the form x^n-1 ??
x^12-1 = (x-1)(x+1)(x^2+1)(x^2-x+1)(x^2+x+1)(x^4-x^2+1)
I need to write a code for that . i was thinking in terms of prime factorizing n then then recursively solving it .. but doesn't work
Can any one help me out with the logic part ?

Thank you
abhijith is offline  
November 7th, 2009, 09:23 AM   #2
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Re: Factorization

Start with something smaller and work you way up.

x^2 - 1 = (x - 1)(x + 1)
x^3 - 1 = (x - 1)(x^2 + x + 1)
x^4 - 1 = (x - 1)(x^3 + x^2 + x + 1) = (x - 1)(x + 1)(x^2 + 1)

Keep going and see if you can observe a pattern. Note how some will factor further than others and so must be accounted for. Since there are differences you will have to separate them into do this this way, and do that that way, depending on the exponent ...but there IS a pattern in the first stage of each.

Try also looking into the geometric series for a similar pattern.
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