The polynomial 2x³ − 4x² + ax + b, where a and b are constants, is denoted by p(x). It is given that when p(x) is divided by (x + 1) the remainder is 4, and that when p(x) is divided by (x − 3) the remainder is 12.

i. Find the values of a and b.

ii. When a and b have these values, find the quotient and remainder when p(x) is divided by (x² - 2).