Factorization of the q-difference equation for continuous q-Jacobi polynomials

The formalism of factorization recently used by Atakishiyev et al ( 2007 J. Phys. A: Math. Theor. 40 9311-7) to study the q-difference equation for continuous q-Hermite polynomials is extended to the continuous q-Jacobi polynomials. Particular cases of continuous q-Laguerre, q-Hermite, q-Legendre and q-ultraspherical polynomials are easily recovered.