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Math Help - Irreducible polynomial

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    Irreducible polynomial

    Write down an irreducible polynomial of degree 3 over the field F3 of 3 elements.

    I have a very vague idea about irreducible polynmials. I think it is one which cannot be factorized completely.

    So if i give an answer to this as x^3 +1, would I be right. or say, 2x^3 +1.
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  2. #2
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    Quote Originally Posted by poorna View Post
    Write down an irreducible polynomial of degree 3 over the field F3 of 3 elements.

    I have a very vague idea about irreducible polynmials. I think it is one which cannot be factorized completely.

    So if i give an answer to this as x^3 +1, would I be right. or say, 2x^3 +1.
    no, both polynomials that you gave have a root in your field. one example is x^3+x^2+2. note that a polynomial of degree 3 over a field is irreducible if and only if it has no root in that field.
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