Hello, can someone answer these two questions? I'm stuck. THANKS!

Exercise 3.3. Consider the field F = Z5. Let f = X 3 +X+ [1] F[X], g = [2]X 2 + [3]X+ [4] F[X], and h = [3]X 2 + [2]X + [1] F[X]. Compute (gh) mod f. Show your work.

Exercise 3.4. Consider the field F = Z5. Use the Lagrange interpolation formula to compute the coefficients of the polynomial g F[X] of degree less than 3 such that

g([1]) = [3], g([2]) = [4], g([3]) = [1].

Show your work.

EXERCISE 3.3. Consider the field F Zg Let f X3HX + [1] FX], g [2x2+13x + [4] and -[3]X2 + [2x + 11je FX]. Compute (gh) mod f. Show your work. F(Xj, EXERCISE 3.4. Consider the field F = Z5. Use the Lagrange interpolation formula to compute the coefficients of the polynomial g E FX] of degree less than 3 such that 3, 9(2 Show your work EXERCISE 3.3. Consider the field F Zg Let f X3HX + [1] FX], g [2x2+13x + [4] and -[3]X2 + [2x + 11je FX]. Compute (gh) mod f. Show your work. F(Xj, EXERCISE 3.4. Consider the field F = Z5. Use the Lagrange interpolation formula to compute the coefficients of the polynomial g E FX] of degree less than 3 such that 3, 9(2 Show your work