Upgrading from:

Algebra`PolynomialExtendedGCD`

New function PolynomialExtendedGCD has been added to the built-in Mathematica kernel.

PolynomialExtendedGCD gives the extended greatest common divisor for two univariate polynomials:

Version 5.2 << Algebra`PolynomialExtendedGCD`;
PolynomialExtendedGCD[x^2 + 2 x + 1, Expand[(x + 1) (x + 2)], 
 Modulus -> 7]