The authors present a relativistic and cross-section factorized framework for computing quasielastic A(p,pN) observables at intermediate and high energies. The model is based on the eikonal approximation and can accommodate both optical potentials and the Glauber method for dealing with the initial- and final-state interactions (IFSI). At lower nucleon energies, the optical-potential philosophy is preferred; whereas at higher energies, the Glauber method is more natural. This versatility in dealing with the IFSI allows one to describe A(p,pN) reactions in a wide energy range. Most results presented here use optical potentials, as this approach is argued to be the optimum choice for the kinematics of the experiments considered in the present paper. The properties of the IFSI factor, a function containing the entire effect of the IFSI, are studied in detail. The predictions of the presented framework are compared with two kinematically different experiments. First, differential cross sections for quasielastic proton scattering at 1 GeV off C-12, O-16, and Ca-40 target nuclei are computed and compared to data from Petersburg Nuclear Physics Institute (PNPI). Second, the formalism is applied to the analysis of a He-4(p,2p) experiment at 250 MeV. The optical-potential calculations are found to be in good agreement with the data from both experiments, showing the reliability of the adopted model in a wide energy range.