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Math Help - monic polynomials

  1. #1
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    monic polynomials

    Can somebody give me hints on these question please?

    (i) List all the monic polynomials over
    F2 of degree =<3.
    (ii) Determine which of these polynomials are irreducible over
    F2.

    (iii) Factorize the reducible polynomials into irreducible polynomials.


    Thanks alot
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  2. #2
    Moo
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    Hello,
    Quote Originally Posted by knguyen2005 View Post
    Can somebody give me hints on these question please?

    (i) List all the monic polynomials over F2 of degree =<3.
    (ii) Determine which of these polynomials are irreducible over F2.
    (iii) Factorize the reducible polynomials into irreducible polynomials.


    Thanks alot
    i) In F_2 the possible coefficients are 0 and 1.
    ii) list them first, then try to see if they can be factored...
    iii) ... if they can, factor them.
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  3. #3
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    Quote Originally Posted by Moo View Post
    ii) list them first, then try to see if they can be factored...
    I want to add something to Moo, angle.

    Those polynomials are factorable if and only if they have zeros.
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