How do i factor the trinomial 2z^2+3z-14

Ok so you do factoring by taking the equation and bringing it down, like this:

2z^2+3z-14
2z           +7      (use multiples of 14 to find 2 numbers that add up to 3)
1z            -2       ( cross multiply 2 and -2 and cross multiply 1 and 7)
(notice how 2*-2 = -4 and 1*7= 7, this comes the the point where you have to add these products, -4+7 which gives you 3, assuring you that the work you did above is correct but instead of doing (2z-2)(1z-2) you have to do it with the one next to it so 2z would go with +7, 1z with -2 so the final answer would be (2z+7)(z-2)

Iknow one of the answers is a and maybe b but not 100% sure about b