1)CONCRETE BATHROOM FLOOR WHERE THERE WAS A CONGOLEUM SHEET GLUED TO THE FLOOR
Using a heat-n-strip tool (looks like an industrial strength hair dryer) softens it up, then I am just hacking it with a trowel, but I might switch to a razor blade on a long stick like was posted here before.
Also the orange cleaner works in spots where it is very thin.
2) GLUE DOWN CARPET FOAM. I rented a floor scrubber with a scarifying brush. You wet the floor and it just turns it into goop. It worked great but be careful to keep the brush flat or it can put ridges into the concrete.