let be a zero of over , Show that splits over

I don't understand this question because is irreducible in ( and ) so how can be its zero.

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- Apr 13th 2009, 06:19 PMfrankdent1splitting over Z mod 2
let be a zero of over , Show that splits over

I don't understand this question because is irreducible in ( and ) so how can be its zero. - Apr 13th 2009, 09:05 PMwhipflip15
The zero does not lie in Z_2. It lies in an extension of Z_2 containing alpha.

To help solve problem note that alpha^2 is also a root in Z_2(alpha). - Apr 13th 2009, 10:31 PMNonCommAlg