2. If $2 x^{2}-6 y^{2}+x y+k x+6$ can be factored into the product of two linear factors, then the number of integer values of $k$ is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
2. B.

Using the discriminant or the method of undetermined coefficients, we get $k= \pm 7$.