A polynomial greatest common divisor of two polynomials 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.
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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.