repair scratches and discolour - black polished porcelain floor

Hi, Probably firstly you want to stop using your hoover in your bathroom, but rather get a damp cloth and wipe it. Depending on how bad is the damage its could be repairable by various methods. For example in my mind you could try to sort this issue with tile polishers such as Tableau Black Tile Polish or similar to it. I would suggest to commit this job to a specialist, because if I assume your grout is white and it would be patched with the black polisher then it would become bigger issue. Hope this helps