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Math Help - Simple polynomial division question

  1. #1
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    Simple polynomial division question

    Hello

    I hope someone can help me with this.

    Let's say I want to divide x^2 + x + 1 into x^2 + 1

    Am I right in thinking the answer is 1 remainder x?

    This is how I am getting my answer...

    I convert my polynomials into binary -

    x^2 + x + 1 = 111
    x^2 + 1 = 101

    Then I do long division -

    Code:
            1
    111 / 101
          111
          ----
          010
    Which translates as 1 remainder x.

    Am I correct?

    If so, how would I handle x^4 + 1 into x^2 + 1?

    Convert to binary -

    10001 / 101

    Am I right in thinking the answer is -

    Code:
              0
    10001 / 101
            000
            ----
            101
    So the answer is 0 remainder x^2 + 1?

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

    I hope someone can help me with this.

    Let's say I want to divide x^2 + x + 1 into x^2 + 1

    Am I right in thinking the answer is 1 remainder x?

    This is how I am getting my answer...

    I convert my polynomials into binary -

    x^2 + x + 1 = 111
    x^2 + 1 = 101

    Then I do long division -

    Code:
            1
    111 / 101
          111
          ----
          010
    Which translates as 1 remainder x.

    Am I correct?

    If so, how would I handle x^4 + 1 into x^2 + 1?

    Convert to binary -

    10001 / 101

    Am I right in thinking the answer is -

    Code:
              0
    10001 / 101
            000
            ----
            101
    So the answer is 0 remainder x^2 + 1?

    Thank you.
    Your answers are correct.

    Your method will work, I think, when the coefficients of both polynomials are either zero or one.
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  3. #3
    Junior Member
    Joined
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    Hi,

    the first part what u did it is correct.

    for the second part that is when x^4+1 divided by x^2+1
    the remainder will be -x^2+1 and quotient is x^2.
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  4. #4
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    Quote Originally Posted by tutor View Post
    for the second part that is when x^4+1 divided by x^2+1
    the remainder will be -x^2+1 and quotient is x^2.
    Hello

    Thanks for the reply.

    I am not too worried about it being -x^2 + 1 or x^2 + 1 (in my code, whether I XOR a minus or a plus, the answer is the same), but I do not understand why the coefficient is x^2.

    I am dividing x^2 + 1 by x^4 + 1. Do you think I am doing it the other way round?

    Thanks
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  5. #5
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    Quote Originally Posted by tutor View Post
    Hi,

    the first part what u did it is correct.

    for the second part that is when x^4+1 divided by x^2+1
    the remainder will be -x^2+1 and quotient is x^2.
    The original question says into, not by .....
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