Use the Euclidean Algorithm to compute the greatest common divisors of the following

Step 1 of 4

Theorem-1: If and are polynomials over a field F, not both the zero polynomial, then there is a unique monic polynomial over F such that

(a) and , and

(b) If  is a polynomial such that and , then

The polynomial is called the greatest common divisor of and

Theorem-2:  If and are polynomials over a field F, not both the zero polynomial, and  is their greatest common divisor, then there exist polynomials and over F such that