 Polynomial greatest common divisor

A polynomial greatest common divisor of two polynomials, not both zero, over a field divides both and is divisible by every common polynomial divisor. It is unique after requiring it to be monic, and the polynomial Euclidean algorithm computes it.

The polynomial greatest common divisor (GCD) refers to the highest degree polynomial that divides two or more polynomials without leaving a remainder. It is the polynomial analog of the greatest common divisor of integers. ### Key Concepts: 1. **Polynomials**: A polynomial is an expression consisting of variables and coefficients, structured as sums of terms, where each term includes a variable raised to a non-negative integer exponent.