The factorized kernel technique for solving neutron transport problems with arbitrary anisotropic scattering is studied and developed numerically. A new derivation that is simple and straightforward is given for the factorization formulas. One-dimensional slab and two-dimensional infinite parallelepiped problems are studied, and extensive results with several useful comparisons are given. Nonclassical Gaussian quadrature rules are constructed with higher order and precision. Different criteria are given to check these rules and calculate the absolute relative error. Several possible applications and extensions are proposed, and the advantages of this approach are demonstrated.