The problem of disturbance rejection and disturbance rejection while decoupling with stability or pole placement is studied using a polynomial matrix approach. Necessary and sufficient conditions for the solvability of the problem of disturbance rejection as well as for the problem of disturbance rejection with input-output decoupling are derived. A number of poles of the closed-loop system are proved to be fixed for both of the above problems, and a procedure for placing all the remaining poles of the closed-loop system is presented.