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Math Help - Find roots of poly in Z_5[x]

  1. #1
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    Find roots of poly in Z_5[x]

    Find roots and factor 3x^4 + x^2 + 1 in Z_5[x]

    Roots:
    f(0) = 1
    f(1) = 0 in Z5
    f(2) = 3 in Z5
    f(3) = 3 in Z5
    f(4) = 0 in Z5

    So Ive only found 2 roots: 1 and 4. How do I find the other two?
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  2. #2
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    Re: Find roots of poly in Z_5[x]

    divide by (x - 1)(x - 4).
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  3. #3
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    Re: Find roots of poly in Z_5[x]

    Yeah I figured it out. What I was hung up on was the fact that while working in Z5 and with a poly of degree 4, it doesn't necessarily imply that there are 4 roots. But thanks for the reply.
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