(i)[5]
The polynomial $x^3 + ax^2 + bx + 8$, with $a$ and $b$ as constants, is called $p(x)$. It is stated that the remainder on dividing $p(x)$ by $(x - 3)$ is $14$, and that the remainder on dividing $p(x)$ by $(x + 2)$ is $24$. Determine the values of $a$ and $b$.
(ii)[4]
With these values of $a$ and $b$, determine the quotient when $p(x)$ is divided by $x^2 + 2x - 8$ and hence solve the equation $p(x) = 0$.