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I need to figure out whether or not the polynomial

[tex]x^6-2x^3-1[/tex]

is irreducible (over Q).

I don't think Eisenstein works in this case, and performing modulo 2 on this i get [tex]x^6-1[/tex]

which is reducible over F2.

Any ideas? Incidently, if i let y=x^3, then i get

[tex]y^2-2y -1[/tex]

which is irreducible over Q.....but i'm not sure if that means anything about the original polynomial.

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# Is this irreducible?

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