3.19: Polynomial factor and remainder

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