The New England Patriots can clinch the AFC East division with:
NE win + NE clinches at least a tie in strength of victory tiebreaker over NYJ OR
NE win + NYJ loss or tie ORNE tie + NYJ loss OR
NE tie + NYJ tie + NE clinches at least a tie in strength of victory tiebreaker over NYJ OR
NYJ loss + NE clinches at least a tie in strength of victory tiebreaker over NYJ
(Note: NE clinches at least a tie in strength of victory tiebreaker in scenarios 1, 4 and 5 if two of the following occur: BUF win, PIT win, MIA loss, CLE loss)
The New England Patriots clinch a playoff spot with:
NE win OR
PIT loss OR
NYJ loss OR
NE tie + KC loss OR
NE tie + PIT tie OR
NE tie + NYJ tie
So basically the Patriots win and they're in. More importantly, the Patriots want the following games to play out:
If any two of the above games happen, and the Patriots win, then New England clinches the AFC East crown, while also helping the Patriots inch closer towards a first round bye.