If your terrazzo floor still looks dull and dirty after you have been cleaned it, please do not be tempted to use a heavy duty cleaner.
As I have already said, when your floor looks dull and dirty, the surface has started to become porous. So you will need specialist equipment and knowledge about cleaning terrazzo to remove the ingrained dirt without damaging your floor.
If you are fortunate your floor may only need a professional deep clean and light polish. However, if your floor is uneven or severely damaged, then your only option is terrazzo floor restoration