  To find boundary contributions is a rather difficult problem when applying
the BCFW recursion relation. In this paper, we propose an approach to bypass
this problem by calculating general tree amplitudes that contain no polynomial
using factorization limits. More explicitly, we construct an expression
iteratively, which produces correct factorization limits for all physical
poles, and does not contain other poles, then it should be the correct
amplitude. To some extent, this approach can be considered as an alternative
way to find boundary contributions. To demonstrate our approach, we present
several examples: $\phi^4$ theory, pure gauge theory, Einstein-Maxwell theory,
and Yukawa theory. While the amplitude allows the existence of polynomials
which satisfy correct mass dimension and helicities, this approach is not
applicable to determine the full amplitude.
