  In this paper, we demonstrate that the factorizations for tree amplitudes in
the double-cover framework, for various theories, can be generated from the
gravity amplitude in the double-cover prescription. Using our method, the
factorized formulae for amplitudes of Yang-Mills theory, special
Yang-Mills-scalar theory, and bi-adjoint scalar theory, have been derived. The
differential operators indicate some non-trivial relationships among
factorizations for above theories, as can be understood through four angles
which are factorization channels, pole-structures, gauge choices, as well as
BCFW recursions.
