We need to solve the quadratic equation:
x^2 - 5 x - 14 = 0 by factoring.
So we look for a pair of factors whose product is -14 and when combined render - 5. So we find the pair "-7 and 2"
Their product = (-7) * 2 = -14
combining them we get: -7 + 2 = -5
So we used them to split the middle term in the equation:
x^2 - 5 x - 14 = 0
x^2 - 7 x + 2 x - 14 = 0
Factor by grouping:
x ( x - 7) + 2 x - 14 = 0
x (x - 7) + 2 (x - 7) = 0
(x - 7) (x + 2 ) = 0
Then for this product to render zero, (x - 7) must be zero (so x = 7)
or (x + 2) is zero (and therefore x = -2)
Then we look for the answers x = -2 or x = 7
This coincides with answer (a) in your list.