1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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 ?

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted