3.13: Coefficients from $p$ and $p'$; remainder of $p''$

The polynomial $p(x) = ax^{3} + bx^{2} + 6x + 4$, where $a$ and $b$ are integers, is divisible by $x - 2$. When $p'(x)$ is divided by $x + 1$ the remainder is $-7$.