In act 3, scene 3, hamlet has an opportunity to kill claudius, but he does not act. one
scene later, however, hamlet does not hesitate at all when he kills polonius in gertrude’s
chamber. why is hamlet able to act in scene 4 but not in scene 3? what does this tell
readers and viewers about hamlet’s character?

Hamlet tends to be indecisive, and this is because he is an over-thinker. As he overanalyzes all sides of a question, this often leads to inaction. In scene 3, Hamlet says that he does not want to kill Claudius because he is praying, and this means that his soul is clean and he would go straight to heaven. However, it is likely that this is an excuse, and that Hamlet cannot bring himself to kill Claudius at that moment. However, he is able to "do so" in the next scene, as it is an impulsive act and he has no time to think about it.

the anecdote makes readers feel sorry for the man’s lack of heritage, then reminds readers that the man has an equally valuable heritage.