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Prove irreducible (p-1)x^p-2 + (p-2)x^(p - 2)x^(p-3) + + 3x^2 + 2x + 1 p=prime

  1. Jul 27, 2010 #1
    show irreducible.. f(x)=(p-1)x^p-2 + (p-2)x^(p-3) + ... + 3x^2 + 2x + 1 (p > 2 is prime)

    hi,
    Does anyone have ideal or hint on the poly. show irred.
    try to us Eisenstein's Irreducibility Criterion, but dot kow how..

    I try it...

    diff(f(x)) = (p-1)(p-2)^p-3 + (p-2)(p-3)x^(p-40 + ... + 3*2^1 + 2

    do't kow how to use diff(f(x)) and f(x)..

    Thanks
     
  2. jcsd
  3. Aug 13, 2010 #2
    Re: prove irreducible.. (p-1)x^p-2 + (p-2)x^(p - 2)x^(p-3) + ... + 3x^2 + 2x + 1 p=p

    Apply Eisenstein's criterion after substituting x=t+1.
     
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