(i)[5]
The polynomial $x^3 + ax^2 + bx + 8$, in which $a$ and $b$ are constants, is represented by $p(x)$. It is given that when $p(x)$ is divided by $(x - 3)$ the remainder is $14$, and that when $p(x)$ is divided by $(x + 2)$ the remainder is $24$. Find the values of $a$ and $b$.
(ii)[4]
When $a$ and $b$ take these values, find the quotient when $p(x)$ is divided by $x^2 + 2x - 8$ and hence solve the equation $p(x) = 0$.