Several days after I have polished a white marble floor there are blotchy light and dark areas. What are these and can I remove them?

The blotchy pattern you are observing is probably moisture. When white marble becomes wet it darkens. When you apply water to the floor , as you do during the polishing procedure, you wet the floor and it darkens. The blotchy appearance will eventually disappear as the tile dries. It may take several days to as long as several weeks for the floor to completely dry.
It is a good idea to use a moisture meter to be sure the problem is in fact moisture. Check the floor in several locations. You may find that the moisture is concentrated around the grout lines. If a moisture meter is unavailable use a hair drier. If the problem is moisture the hair dryer should dry the marble and the blotchy pattern should disappear.