glue removal from cement floor

I have removed both carpet and linoleum from a cement floor. They were installed about 25 years ago. I have some questions about how to remove the glue left from the rug and the glue and backing left from the linoleum. Any help in this area would be appreciated.

If I choose not to remove the glue, could I just lay backer board over the existing floor without attaching it, seal the seams of the backer board, and install the tile over the top of the backer board.

Any help would be appreciated - Thanks

I have some questions about how to remove the glue left from the rug and the glue and backing left from the linoleum. Any help in this area would be appreciated.

Soak it with water and scrape it.

If I choose not to remove the glue, could I just lay backer board over the existing floor without attaching it, seal the seams of the backer board, and install the tile over the top of the backer board.

That's a joke question right?
Are you kidding me?
Seriously - there is no way that will work.

You can clean up the remnants easy enough, it takes a little effort but it can be done.