A polynomial in x leaves remainders 2 and 3 when divided by x + 1 and x - 1 respectively. Then the remainder we get when that polynomial is divided by $$x^2 - 1$$ is

A

$$\frac{3x + 2}{2}$$

B

$$\frac{3x - 2}{2}$$

C

$$\frac{x - 5}{2}$$

D

$$\frac{x + 5}{2}$$