Why is this relation not in Boyce-Codd Normal Form (BCNF)?
C is a non-prime attribute (not part of the candidate key), and C depends on (A,B), which is a proper subset of the candidate key.

So the table is not in second normal form by definition.

Since BCNF implies 3NF and 3NF implies 2NF, this implies that the table is not in BCNF.