3.17: Three conditions on a cubic; unique real root

The polynomial $p(x)$ is such that $p(x) = ax^{3} + bx^{2} + cx - 5$, where $a$, $b$ and $c$ are integers. It is given that $p'(0) = 12$. It is also given that $p(x)$ has a factor of $3x - 1$ and a remainder of $95$ when divided by $x - 2$.