X-Factor is a name used by multiple teams.
The original X-Factor posed as mutant hunters, using this as a cover to help mutants, while assuming a mutant-activist identity as the X-Terminators.
The second X-Factor was a government-sponsored mutant superhero group, under Val Cooper's authorities, and employing in-probation mutant criminals.
Most of that roster was recruited into Madrox's X-Factor Investigations, a detective agency who was as well in contact with Val Cooper.
The name was bought back from Madrox by Harrison Snow and used for an X-Factor team funded by Serval Industries.
X-Factor Investigations was reformed under Northstar's leadership to assist The Five of Krakoa in resurrecting dead mutants without violating the Resurrection Protocols.
Note:The X-Factor is also a term used to described the X-Gene.