Let R be an associative ring with identity, C(R) denote the center of R and g(x) be a polynomial in C(R)[x]. We introduce the new notion of g(x)-f-clean rings, as a generalization of g(x)-clean rings. R is called g(x)-f-clean if every element r ∈ R can be written as r = s + w with g(s) = 0 and w a full element of R. In this paper, we study some general properties of g(x)-i-clean rings.