The polynomial f(x) = ax³ + 7x² – 9x + b is divisible by 2x – 1. The remainder when f(x) is divided by x – 2 is 5 times the remainder when f(x) is divided by x + 1.

i. Show that a = 6 and find the value of b.

ii. Using the values from part a, show that f(x) = (2x – 1) (cx² + dx + e), where c, d and e are integers to be found.

iii. Hence factorise f(x) completely.