Using Eisenstein to prove irreducibility in Q

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Homework Statement


Use Eisenstein's criterion to show that 2*x^4 - 8x^2 + 3 is irreducible in Q[x]


Homework 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


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.
 

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