Hello all I'm teaching myself cryptography, and I'm struggling with polynomial arithmetic over finite fields. I've some what been able to teach myself how to do the arithmetic over $GF(2)$, but when the finite field increase to higher numbers like $GF(101)$ I struggle with long division aspect as it relates to the 101. The specific question I'm struggling with is to determine the GCD of the polynomials: $x^5 + 88x^4 + 73x^3 + 83x^2 + 51x + 67$ and $x^3 + 97x^2 + 40x + 38$ over $GF(101)$.
I'm a little new on this site so I still need to learn how to structure questions. Any help would be great