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    Algebraic Number Theory

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    Explain why the polynomial H(x) = x^5 + x^4 + x^3 + x^2 + 1 is irreducible over the integers.

    © BrainMass Inc. brainmass.com March 4, 2021, 8:43 pm ad1c9bdddf
    https://brainmass.com/math/number-theory/algebraic-number-theory-189090

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    Update:

    I noted the restrictions on the method to be used for solving this question.

    The problem can be easily solved using the Rational Roots Theorem alone (Without using Descartes' Rule of Signs) as ...

    Solution Summary

    Explanation of why the given polynomial is irreducible over integers using the Rational Roots Theorem.

    $2.49

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