The expression for the neutron escape probability from an absorbing body has been expressed in terms of two polynomials. The main feature of these polynomials is that only the coefficients depend on the shape of the geometry while the expressions remain same. At the same time, the resulting expressions for the escape probability ensure the correct behavior in the white and black limits. As examples, numerical results are presented for five geometries: a sphere, a slab, an infinite solid cylinder, a two-dimensional square geometry having infinite height, and a three-dimensional cuboid. The results obtained by using these polynomials match very well with the exact results obtained by using the program POLM, which solves numerically the exact expressions for the escape probability for the respective geometries.