  Spinor polynomials are polynomials with coefficients in the even sub-algebra
of conformal geometric algebra whose norm polynomial is real. They describe
rational conformal motions. Factorizations of spinor polynomial corresponds to
the decomposition of the rational motion into elementary motions. Generic
spinor polynomials allow for a finite number of factorizations. We present two
examples of quadratic spinor polynomials that admit infinitely many
factorizations. One of them, the circular translation, is well-known. The other
one has only been introduced recently but in a different context. We not only
compute all factorizations of these conformal motions but also interpret them
geometrically.
