1965 AHSME Problem 27

When y^2 + my + 2 is divided by y - 1 the quotient is f(y) and the remainder is R_1. When y^2 + my + 2 is divided by y + 1 the quotient is g(y) and the remainder is R_2. If R_1 = R_2 then m is:

\textbf{(A)}\ 0 \qquad \textbf{(B) }\ 1 \qquad \textbf{(C) }\ 2 \qquad \textbf{(D) }\ - 1 \qquad \textbf{(E) }\ \text{an undetermined constant}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.