3.28: Cubic factor and midpoint of intersection points

Show that $x + 3$ is a factor of $x^{3} + 2x^{2} - 23x - 12$.

The curve $y = x^{3} + 2x^{2} - 33x - 5$ and the line $y = 10x + 7$ intersect at $A$, $B$ and $C$, with the $x$-coordinate of $A$ least and of $C$ greatest. Show that $B$ is the midpoint of $AC$.