Suppose that we've been given two polynomials and we want to find their Greatest Common Divisor. For integers, we have the Euclidean algorithm which gives us the G.C.D of the two given integers. Could we generalize the Euclidean algorithm to be used to find the G.C.D of any two given polynomials using long division?(adsbygoogle = window.adsbygoogle || []).push({});

If yes, how? For example I want to show that x+1 and x^{2}+5x+6 are two co-prime polynomials. How could I do that? And can I ultimately find a way to represent this fact using the Bezout's theorem? (I mean can I finally find A and B as two polynomials that we have A(x+1) + B(x^{2}+5x+6) = 1?)

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# Is it always possible to find the G.C.D of two polynomials?

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