  We show that the group cohomology of torsion-free virtually polycyclic groups
and the continuous cohomology of simply connected solvable Lie groups can be
computed by the rational cohomology of algebraic groups. Our results are
generalizations of certian results on the cohomology of solvmanifolds and
infra-solvmanifolds. Moreover as an application of our results, we give a
simple proof of the surprising cohomology vanishing theorem given by
Dekimpe-Igodt.
