  We discuss existence of factorizations with linear factors for (left)
polynomials over certain associative real involutive algebras, most notably
over Clifford algebras. Because of their relevance to kinematics and mechanism
science, we put particular emphasis on factorization results for quaternion,
dual quaternion and split quaternion polynomials. A general algorithm ensures
existence of a factorization for generic polynomials over division rings but we
also consider factorizations for non-division rings. We explain the current
state of the art, present some new results and provide examples and counter
examples.
