Consider the following recurrence T (n) = 4T (n/2) + n^2 log n, T (1) = 1.

(a) (2 points) Can the masters theorem be applied to solve this recurrence? If yes, apply it. If not, formally explain the reason why.

(b) (4 points) Solve the above recurrence using the recursion tree method.

(c) (4 points) Formally verify that your answer from part (b) is correct using induction.

(d) (5 points) Solve the above recurrence exactly using domain-range substitution.