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Galois Theory : Show the Galois group of (x^2-2)(x^2+2) over Q (rationals) is isomorphic to Z_2xZ_2 (Direct product group of integers modulo 2).

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Show the Galois group of (x^2-2)(x^2+2) over Q (rationals) is isomorphic to Z_2xZ_2 (Direct product group of integers modulo 2).

For your choice of your mapping theta, that is operation preserving, 1 to 1, and onto please show that is well defined.

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Solution Summary

A Galois group is investigated. The solution is detailed and well presented.

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