I am working inch by inch on an entire basement floor of concrete to remove the old black rubber backing left after removing years old shag carpeting. Is there some method or product I can use to speed up the process - scraping only is tedious project. Any suggestions appreciated.

Scraping is the best way unless you can have it shot-blasted.

Do not use chemicals, you will make a mess and using chemicals in a basement is never a good idea. Over time the residual chemical will pollute the air.