Recall that a group G is called polycyclic-by-finite (or virtually polycyclic) if there exists a normal subgroup of finite index $N$ in $G$ such that $N$ is polycyclic.
I know that a free group of finite rank $r>1$ is not a polycyclic group because it is not solvable.
My question is that :
Is a free group of finite rank $r>1$ polycyclic by finite?
Thanks.