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Eisenstein Criterion

  1. May 3, 2017 #1
    1. The problem statement, all variables and given/known data
    Determine the irreducibility ##x^2 - 12##

    2. Relevant equations


    3. The attempt at a solution
    By using ##p=3## we see that ##x^2 - 12## is irreducible, because 3 does not divide 1, and 9 does not divide 12. That's easy enough.
    But what if I have ##x^2 - 16##? Obviously this is factorable, but using p=3, doesn't the Eisenstein criterion tell us that it is irreducible?
     
  2. jcsd
  3. May 4, 2017 #2

    fresh_42

    Staff: Mentor

    No, because you cannot apply Eisenstein here: ##3 \nmid 16 = a_0##.
     
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