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    Irreducible Polynomials

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    Prove that a polynomial f(x) of degree 2 or 3 over a field F is irreducible if and only if f(a) different of 0 for all a belongs F.
    Hint: Use the following theorem that a polynomial f(x) has x-a as a factor if and only if f(a)=0.

    Please can you explain this step by step. and Can you give me examples.

    Can you explain why this does not happened with polynomial of degree 4?

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    https://brainmass.com/math/number-theory/solving-irreducible-polynomials-103918

    Solution Preview

    "Lemma A" = the theorem offered in the Hint

    Lemma B:
    If a polynomial of degree 2 or 3 is reducible at least one of its factors must ...

    Solution Summary

    Irreducible polynomials are investigated and relevant questions are explained in the solution..

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