1.9: Coefficients from a factor and a remainder

A polynomial $p(x)$ is $ax^{3} + 8x^{2} + bx + 5$, where $a$ and $b$ are integers. It is given that $2x - 1$ is a factor of $p(x)$ and that a remainder of $-25$ is obtained when $p(x)$ is divided by $x + 2$.