Many thanks for all these ideas. I have a fake marble sink/counter in my master bath and the bottom of the sink is terrible. Scrubbing does no good for it, seems to have a lot of junk stuck in it all over. I've scraped and put chemicals in it and rubbed and scrubbed with metal pads, still looks terrible like it hadn't been touched since it was installed in the mid 1970s.
I'll try all these, one at a time.