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Factorisation of x^22 -3x^11 +2

  1. Apr 29, 2007 #1
    factorize [tex] x^{22} -3x^{11} + 2 [/tex]

    right so I have p(x) = (x^11 -2)(x^11 - 1)

    (x^11 -2) satifies eisentstein, obviously x-1 is a factor of the second factor. Long division reaps [tex] x^{10} + x^9 +...+x + 1 [/tex]

    the solution asserts that this is also irreducible, but I do not see this?? Is this one of those where you substitue x for y+1??
    Last edited: Apr 29, 2007
  2. jcsd
  3. Apr 29, 2007 #2


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    Formatting tip: use curly braces {} to group the entire exponent together as one unit.
  4. Apr 29, 2007 #3


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    Yea, any polynomial of the form (x^p-1)/(x-1) can be shown to be irreducible by making the substitution y=x+1 and applying Eisenstein's criteria. You have to do a little work with binomial coefficients, and it's probably easier to prove this general case then the case p=11.
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