I made another attempt at checking the cog wheel icon on the bottom of the login screen on the Facebook app and, much to my surprise, the option to "Remoce account from iPad" is now listed as an option. Problem solved.
When I open the Facebook App on my iPad, a blue screen appears with the profile picture and name of several accounts. On the bottom of the screen I have the options to click on a small cog icon, which lists each account and the login settings, click on the text "Log Into Another Account", or click on the text "Sign Up For Facebook". What I want to know is how can I remove one of the accounts from the login screen?