You can use a Routh–Hurwitz matrix to stabilize the system.
A Routh–Hurwitz matrix is a method for checking wheather or not a system is stable. It can also be used to stabilize the system by giving you a new denominator function for G(s).
According to this method, a system will be stable if the first column of the Routh–Hurwitz matrix contains only positive values.
You can stabilize the system by introducing a gain k and re-calculate the Routh–Hurwitz matrix to determine this k value that makes the system stable. In other words you can stabilize the system by inteoducing feed-back into it to conpensate for the unstable components of G(s).
Check these additional resources if you're still unsure about how to do this: