Remark
This requires that you factor all 4 choices. There is no other way to do it. However you can eliminate one of the choices.
C might give you a factor of 1/7 but it will not give you 7. The same can be said about a and b. They do factor, but you will get a fraction in both answers. That means your answer is probably D, which we should check out first.
Solution
x ^2 - 3x - 28 = 0
(x - 7)(x + 4) = 0 These factors come about because the numbers 4 and 7 are relatively close together. Your other choices for factors would be 2 and 14 or 1 and 28. These numbers are just too far apart when subtracted to be the answer.
x - 7 = 0
x = 7
x + 4 = 0
x = - 4
D is indeed your answer.
C
No factors will work. This cannot be factored into integer results.
B
4x^2 - 49 Use the difference of squares.
(2x - 7)(2x + 7)
x = 7/2 or x = -7/2 Not a choice
A
(x + 1)(4x - 11) =0
x= - 1 or
x = 11/4
A is not the answer