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    Irreducible Polynomials

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    Let f(x) = x^4 − 8x^3 + 12x^2 − 6x + 2. Show that f(x) is irreducible over
    the field of rational numbers.

    I know that it can't be factored... but how do I show its irreducible?

    © BrainMass Inc. brainmass.com October 5, 2022, 6:26 pm ad1c9bdddf

    Solution Preview

    We can use the Eisenstein's Irreducibility Criterion.

    Let p=2, then p is a prime. We ...

    Solution Summary

    Irreducible polynomials are investigated. The Eisenstein's irreducibility criterions are examined.