3.30: Polynomial factor and remainder

The polynomial $p(x) = mx^{3} - 29x^{2} + 39x + n$, where $m$ and $n$ are constants, has a factor $x - \dfrac{1}{3}$, and remainder $6$ when divided by $x - 1$. Show that $x - 2$ is a factor of $p(x)$.