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.