The given trinomial is
8x^2 + 2x - 3
We would factor it by applying the method of factorisation. We would find two numbers such that their sum or difference is 2x and their product is - 24x^2. The numbers are 6x and - 4x. It becomes
8x^2 + 6x - 4x - 3
2x(4x + 3) - 1(4x + 3)
(2x - 1)(4x + 3)
Looking at the given options, the factor of this trinomial is option A.