3.31: Find coefficients from factor and remainder

It is given that $p(x) = ax^{3} - 7x^{2} - bx + 9$, where $a$ and $b$ are constants.
$x + 3$ is a factor of $p(x)$.
When $p(x)$ is divided by $x + 2$ the remainder is $-35$.
Find the values of $a$ and $b$.