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Irreducible polynomial

  1. Oct 23, 2005 #1
    let F be a field with char p. Let a, b be in the field, with a not equal b^p .
    show that f(x) = x^p - a is irreducible

    i was thinking to start by contradiction
    assume f(x) is not irreducible....than f(x) = (x-a1)(x-a2)....(x-an)
    where no a can be equal to a p th power of b.
    in order for the polynomial to be irreducible i would need to check that every number smaller than p and which is not a pth power of some b, is not a root of f(x). I dont really know how to proceed from here...can anyone give me a hint.. or maybe suggest a different proof ?

    thnx
     
  2. jcsd
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