Additional modem in large house?

Our house is pretty spread out. The cable modem is at the far eastern end of the house, and most of the house is able to get wifi fine. However, the room at the far west end barely gets a signal. We've bought two range extenders in the last three months, and each one has helped some for a while and then gone dead. Is it possible to get a second wired connection at the other end of the house, kind of the way you would add another cable box to get TV? We already have a working cable in that room that we're not using (i.e., it gets cable TV, but we don't watch TV in that room, so we could use it if that is possible). So could we just buy another cable modem, hook it up to that live cable, and go? Would we need a second internet order? How might this work?

Any help you could give would be appreciated. Thanks!