  Based on the Bezout approach we propose a simple algorithm to determine the
{\tt gcd} of two polynomials which doesn't need division, like the Euclidean
algorithm, or determinant calculations, like the Sylvester matrix algorithm.
The algorithm needs only $n$ steps for polynomials of degree $n$. Formal
manipulations give the discriminant or the resultant for any degree without
needing division nor determinant calculation.
