Let R be a noncommutative prime ring of char (R) , 2 with Utumi quotient ring U and extended centroid C and I a nonzero two sided ideal of R. Suppose that F(ǂ0), G and H are three generalized derivations of R and f (x1, . . . , xn) is a multilinear polynomial over C, which is not central valued on R. If F(G( f (r)) f (r) − f (r)H( f (r))) = 0 for all r = (r1, . . . , rn) ∈ Iⁿ, then we obtain information about the structure of R and describe the all possible forms of the maps F, G and H. This result generalizes many known results recently proved by several authors ([1], [4], [5], [8], [9], [13], [15]).