Question

Factor: 2xy + 6x - 4y - 12

a)(2x + 4) (y + 3)
b)(2x - 4) (y + 3)^2
c)(2x - 4) (y - 3)
d)(2x - 4) (y + 3)

Answer 1

2x(y+3)-4(y+3)
(2x-4)(y+3)
so the answer is d

Answer 2

(a) and (c) give a constant term of +12, so it cannot be right. (b) gives a constant term of -4*3²=-36...not good.
The only candidate (d) can be confirmed by expansion (multiplication).