Use the Master theorem to find Θ bounds for each of the recurrence relations below. If the Master theorem does not apply, say so and explain why. You need to justify your answers to get full credit for this question. If you are applying Case 1 or Case 3 of the Master theorem, you need to show that one of the functions grows polynomially faster than the other and specify the ϵ for which it is true. If you are applying Case 3 of the Master theorem, make sure to check the regularity condition.
(a) T(0) = T(1) = C1
T(n) = 8T(n/2) + n³ + n*log n + 2ˡᵒᵍⁿ
(b) T(0) = T(1) = C1
T(n) = 2T(n/4) + n³/²
(c) T(0) = T(1) = C1
T(n) = 9T(n/3) + n³ + n² log n

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explanation: