3.18: Factor and remainder; unique real root

The polynomial $P$ is given by $P(x) = ax^{3} + bx^{2} + 3x + 2$, where $a$ and $b$ are integers. $P(x)$ has a factor of $2x + 1$. $P(x)$ has a remainder of $-6$ when divided by $x + 1$.