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Using Eisenstein to prove irreducibility in Q

  1. Apr 2, 2013 #1
    1. The problem statement, all variables and given/known data
    Use Eisenstein's criterion to show that 2*x^4 - 8x^2 + 3 is irreducible in Q[x]


    2. Relevant equations
    Eisenstein's criterion states that a polynomial is irreducible in Q[x] if the following three conditions are met for a prime p.
    (i) p divides all coefficients except a_n and a_0.
    (ii) p does not divide a_n
    (iii) p^2 does not divide a_0


    3. The attempt at a solution
    The only prime that divides all coefficients except a_n and a_0 is 2. However, 2 does divide a_n, but its square does not divide a_0.
     
  2. jcsd
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