I want to show that x^{4}-22x^{2}+1 is irreducible over Q. I believe I need to use the Eisenstein criterion, but Im not really sure how.
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Hi, You're right. Use the Eisenstein criterion to show the polynomial has no linear factors. Then proceed:
Originally Posted by jquinc21 I want to show that x^{4}-22x^{2}+1 is irreducible over Q. I believe I need to use the Eisenstein criterion, but Im not really sure how. Or you could just do this: Let which makes your equation Clearly none of these linear factors is rational, so your quartic can not be reduced over the rationals.
Ah, I knew I was missing something. Usually our Eisenstien problems are simpler, so I figured there would be a nice trick. By the way, I love your name
Hi Prove It, I don't quite follow your argument (at least the last few lines). with none of the linear factors in Q[x]. So the polynomial is irreducible over the rationals? But and so the polynomial is reducible in Q[x].
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