(8 pts.) Determine the multiplicative inverse ofx, x, 1 in GF(24), using the prime (irreducible) polynomial mx)-+x+1 as the modulo polynomial. (Hint Adapt the Extended Euclid's GCD algorithm on pages 40, 41 of the notes to polynomials) 4. the Extended Euclid's GCD algorithm on Notes slides 40, 41 to polynomials, ic, use x)-x+x+1 in place of im and use the polynomial++1 in place of b in the algorithm. and apply "polynomial division" instead of integer division for numbers. Otherwise, the algorithm follows the same steps, and terminates quickly, ie, the algorithm runs fast since in each iteration of the algorithm, the reminder polynomial's degree will decrease by at least one and, therefore, the reminder polynomial's degree will because zero eventually in the worst case i.e., the final reminder polynomial will be equal to a constant 1 if the two polynomials are relatively prime to each other) Extended Euclid's GCD Algorithm EXTENDED EUCLID (m, b) (B1, B2, B3) (0, 1, b) 2. if B3-0 return A3gcd (m, b) no inverse 3. if B3-1 return B3gcd (m, b B2b mod m 4. Q A3 div B3 5. (T1, T2, T3)=(Al -Q B1, A2 - B2, A3 -Q B3) 6. (A1, A2, 7. (B1, B2, 8. goto 2 A3)m(B1, B3)=(T1, B2, T2, B3) T3) Note: The "div" operator used in Step 4 means "integer division" and returns the quotient. Calculating Multiplicative Inverse of 550 in GF(1759)