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Math Help - Polynomials in integer rings

  1. #1
    pkr
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    Polynomials in integer rings

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  2. #2
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    For #2 a polynomial of degree less than 5 is written as a+bx+cx^2+dx^3 where a,b,c,d\in \mathbb{Z}_2. For each a,b,c,d we have two choices either 0 or 1 since we are working in \mathbb{Z}_2[x]. Therefore, there are 2^4 = 16 such polynomials. For #3 do you know how to apply the division algorithm?

    EDIT: Error! It should have been a+bx+cx^2+dx^3+ex^5 and in that case we have 2^5 =32.
    Last edited by ThePerfectHacker; December 3rd 2008 at 05:58 PM.
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  3. #3
    Senior Member JaneBennet's Avatar
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    There are actually 2^5=32 polynomials of degree less than 5.
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    Senior Member vincisonfire's Avatar
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    For exercice #3, do a division. Method is the same as with integers.
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  5. #5
    pkr
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    Quote Originally Posted by ThePerfectHacker View Post

    EDIT: Error! It should have been a+bx+cx^2+dx^3+ex^5 and in that case we have 2^5 =32.
    I presume you meant ex^4?

    Thanks for the help, will get back to you on q3, too early atm and I have a linear alegebra test soon
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  6. #6
    pkr
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    Done the division, worked great, many thanks.
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