Okay...what is the carpet backing made of. Is it a foam backing or what looks like just the bare carpet weaving?
Glued-down carpet can be a pain to remove. You are correct. The way to remove it is to cut it in strips maybe 12-16 inches wide, get a pliers, and go for it. The width of the workable strips depends on how much the carpet is fighting back. Some is easy to remove - some not.