Use the result of Exercise 5 to factorize each of the following into a constant and monie irreducibles.

(a) 3x2 + 4x + 3 in Z5[X],

(b) 2x3 + 2x2 + X + 2 in Z3[X],

(c) X 3 + 4x2 + X + 1 in Z7[X],

(d) x 3 + 2x2 + 2 in Z3[X],

(e) 2x2 + 3x + 4 in Z7[X],