Exercises for in class

Copy the procedures my_igcdex and my_quo_rem to another worksheet. Rename my_igcdex into my_gcdex, and modify it so that it will do the Extended Euclidean Algorithm not in the integers Z but in the polynomials Q[x]. Then, like inverse_mod_p in the worksheet, use it to write a procedure inverse_mod_f where f is a polynomial in Q[x].
Use your inverse_mod_f to calculate 1/(x³+5) modulo x⁴+7x-9. Then compare your result with Maple. Note: to do this comparison type:
alpha := RootOf(x^4+7*x-9, x); evala( 1/(alpha^3+5) );