1.10.19 Polynomials

condition: Using the Euclidean algorithm, select the polynomials \( M_{1}(x) \) and \( M_{2}(x) \) so that \( f_{1}(x) M_{2}(x)+f_{2}(x) M_{1}(x)=\delta(x), \quad \) where \( \delta(x)- \) greatest common divisor \( f_{1}(x) \) and \( f_{2}(x) \) \[ F_{1}(x)=x^{4}+2 x^{3}-x^{2}-4 x-2, \] \[ F_{2}(x)=x^{4}+x^{3}-x^{2}-2 x-2 \]