This paper is a self-contained discussion of a right factorization approach in the stability analysis of the non-linear continuous-time or discrete-time, time-invariant or time-varying, well-posed unity-feedback system S1(P, C). We show that a well-posed stable feedback system S1(P, C) implies that P and C have right factorizations. In the case where C is stable, P has a normalized right-coprime factorization. The factorization approach is used in stabilization and simultaneous stabilization results.