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February 13th, 2011, 09:12 AM   #1
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Irreducible polynomial over Q

I know about how to show that a polynomial is irreducible over Q using Eisenstein's criterion. But this does not work all the time. For instance, the polynomial:

f(x) = x^3+3x^2-5x+4

Is irreducible over Q, but Eisenstein's criterion does not work here. Are there any other methods of showing that it is irreducible? Does these perchance involve what degrees g and h could have if f = g*h ?
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