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Math Help - Irreducible factorization

  1. #1
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    Irreducible factorization

    For any prime p, describe the irreducible factorization of f(x) = xp-x over Z/pZ.

    Please, help with this problem. I don't even know how to start it.

    Thank you
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  2. #2
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    Re: Irreducible factorization

    Hi,
    Don't you know that ap = a for any a in Zp? So what are the roots of your polynomial in Zp?
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  3. #3
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    Re: Irreducible factorization

    Ok, I know that x=0 and x=0(modp) are roots of the polynomial. I think I am overhinking the question. I am not sure what they want me to describe when they say describe the irreducible factorization.

    Thanks for your help.
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  4. #4
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    Re: Irreducible factorization

    Okay, here's the solution you're trying to find:

    Irreducible factorization-mhfpolynomial.png
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  5. #5
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    Re: Irreducible factorization

    Thank you.
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