  In this paper, we describe geometrical constructions to obtain triangulations
of connected sums of closed orientable triangulated 3-manifolds. Using these
constructions, we show that it takes time polynomial in the number of
tetrahedra to check if a closed orientable 3-manifold, equipped with a minimal
triangulation, is reducible or not. This result can easily be generalized to
compact orientable 3-manifolds with non-empty boundary.
