1.10.3 Polynomials

Problem: Find GCD of polynomials \( f(x), g(x) \in \mathrm{F}_{2}[x] \), where \[ \begin{array}{l} f(x)=x^{7}+x^{5}+x^{4}+x+1, \\ g(x)=x^{8}+x^{6}+x^{5}+x^{4}+x^{3}+x^{2}+1 . \end{array} \]