I dont care about the AP or coaches polls. It's either done by people who have never played (AP) or by some low level staffer in athletic department (coaches)...
I don't really care either. CFP is the one people think matters the most. That said, technically the NCAA does not decide a national champion at all. If you look at the NCAA Football Subdivision Record book they have a list of "major selectors" of national championships and their selections of national champions over the years. These recognized selectors have had several different approaches: polling/math/individual research (only one major selector)/hybrid/playoff.
Also, while like most everyone else I feel the CFP is the real championship, the NCAA also publishes a list of "consensus national champions" which are the winners of the AP, USA Today, Football Writers/National Football Foundation/College Football Hall of Fame poll. These polls can have split national champions and they are still published and recognized by the NCAA. Last time this happened was 2003 when LSU was BCS Champion, and the USA Today champion, while USC was the AP Champion.
Here's what the record book says under the BCS chapter:
"2003—Oklahoma led the BCS rankings going in to the bowl games with a 5.11 mark, LSU was second at 5.99 and Southern California was third at 6.15. LSU captured the BCS title by defeating Oklahoma, 21-14, in the matchup of No. 1 against No. 2 in the Sugar Bowl. However, in the Associated Press (media) final poll, Southern California was voted No. 1 while LSU was No. 1 in the USA Today/ESPN (coaches) final poll."
And here is what it says under the consensus national champions list:
2003 LSU (NFF, USA/ESPN) Southern California (AP, FW)