We present a model that explores the influence of persuasion in a population of agents with positive and negative opinion orientations. The opinion of each agent is represented by an integer number k that expresses its level of agreement on a given issue, from totally against k=-M to totally in favor k=M. Same-orientation agents persuade each other with probability p, becoming more extreme, while opposite-orientation agents become more moderate as they reach a compromise with probability q. The population initially evolves to (a) a polarized state for r=p/q>1, where opinions' distribution is peaked at the extreme values k=±M, or (b) a centralized state for r<1, with most opinions around k=±1. When r»1, polarization lasts for a time that diverges as rMlnN, where N is the population's size. Finally, an extremist consensus (k=M or -M) is reached in a time that scales as r-1 for r«1.