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Math Help - GCD of polynomials

  1. #1
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    GCD of polynomials

    Hello,
    could you help me understand the procedure of finding the GCD of two polynomials step by step, using the Euclidean Algorithm?
    For example
    a = x^3 - 3x +2 , b = x - 1
    Thanks.
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  2. #2
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    Quote Originally Posted by drthea View Post
    Hello,
    could you help me understand the procedure of finding the GCD of two polynomials step by step, using the Euclidean Algorithm?
    For example
    a = x^3 - 3x +2 , b = x - 1
    Thanks.
    There is no need to use Euclidean here and besides it does not work since it produces the answer in the first line.
    Therefore, it does not give any infromation in this problem.

    Just note (x^3 - 3x + 2) = (x-1)(x^2  + x - 2) by long division.
    Thus, \gcd = x-1
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  3. #3
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    Hi and thanks for your answer.
    Could you give me an example of where the Euclid's algorithm can be used,
    concerning polynomials? Should they be polynomials of higher degree?
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  4. #4
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    Quote Originally Posted by drthea View Post
    Hi and thanks for your answer.
    Could you give me an example of where the Euclid's algorithm can be used,
    concerning polynomials?
    When using the Euclidean algorithm you repeating apply the division algorithm in several steps until you get rid of the remainder. The problem here is that first application already produces no remainder. That is why this is not a good example.

    Should they be polynomials of higher degree?
    Look at this.
    It has examples for both numbers and polynomials.
    Both are extremely cases similar.
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