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Math Help - Polynomial multiplication: which of these two answers are correct?

  1. #1
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    Polynomial multiplication: which of these two answers are correct?

    Hello

    I was hoping someone could tell me which of these two answers are correct.

    Question:

    Multiply the following polynomials:

    (x^7 + x^5 + x^3 + x) * (x^27 + x^15 + x^13 + x^12 + x^11 + 1)

    The answer:

    x^34 + x^32 + x^30 + x^28 + x^22 + 2x^20 + x^19 + 3x^18 + x^17 + 3x^16 + x^15 + 2x^14 + x^13 + x^12 + x^7 + x^5 + x^3 + x

    Now, let's say I want to reduce this modulo 2. Should it become -

    A: x^34 + x^32 + x^30 + x^28 + x^22 + x^19 + x^18 + x^17 + x^16 + x^15 + x^13 + x^12 + x^7 + x^5 + x^3 + x

    or

    B: x^34 + x^32 + x^30 + x^28 + x^22 + x^19 + x^17 + x^15 + x^13 + x^12 + x^7 + x^5 + x^3 + x

    I think perhaps it should become A, as 3 modulo 2 is 1.

    What do you think?

    Thank you
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  2. #2
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    Quote Originally Posted by MrSteve View Post
    Hello

    I was hoping someone could tell me which of these two answers are correct.

    Question:

    Multiply the following polynomials:

    (x^7 + x^5 + x^3 + x) * (x^27 + x^15 + x^13 + x^12 + x^11 + 1)

    The answer:

    x^34 + x^32 + x^30 + x^28 + x^22 + 2x^20 + x^19 + 3x^18 + x^17 + 3x^16 + x^15 + 2x^14 + x^13 + x^12 + x^7 + x^5 + x^3 + x

    Now, let's say I want to reduce this modulo 2. Should it become -

    A: x^34 + x^32 + x^30 + x^28 + x^22 + x^19 + x^18 + x^17 + x^16 + x^15 + x^13 + x^12 + x^7 + x^5 + x^3 + x

    or

    B: x^34 + x^32 + x^30 + x^28 + x^22 + x^19 + x^17 + x^15 + x^13 + x^12 + x^7 + x^5 + x^3 + x

    I think perhaps it should become A, as 3 modulo 2 is 1.

    What do you think?

    Thank you
    Yes its A. And you have to use 3 mod 2 is 1
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