  We find explicit free resolutions for the $\scr D$-modules ${\scr D} f^s$ and
${\scr D}[s] f^s/{\scr D}[s] f^{s+1}$, where $f$ is a reduced equation of a
locally quasi-homogeneous free divisor. These results are based on the fact
that every locally quasi-homogeneous free divisor is Koszul free, which is also
proved in this paper
