  We present a new algorithm to decompose generic spinor polynomials into
linear factors. Spinor polynomials are certain polynomials with coefficients in
the geometric algebra of dimension three that parametrize rational conformal
motions. The factorization algorithm is based on the "kinematics at infinity"
of the underlying rational motion. Factorizations exist generically but not
generally and are typically not unique. We prove that generic multiples of
non-factorizable spinor polynomials admit factorizations and we demonstrate at
hand of an example how our ideas can be used to tackle the hitherto unsolved
problem of "factorizing" algebraic motions.
