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Irreducible Polynomials

Characters are:

Q. Z(2)[x] (mod 2), Z[x], Q, Z(2), Z(3), Z(5), Z(9). all mods

? Decide, giving your reasons, which of the following polynomials is irreducible over . Factorize those polynomials that are reducible into a product of irreducible factors.

a)
b)
c)

? Find, with justification, all monic irreducible cubics in .
? Find, with justification, a polynomial in that is irreducible over but not over .

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Solution Summary

Irreducible polynomials are investigated.

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