What scene from act iii do most agree is the climax of hamlet? 1) when hamlet kills polonius 2) when hamlet is unable to kill claudius 3) when hamlet contemplates suicide for a second time 4) when king claudius runs from the room during the play within the play

I believe the correct answer is 1) When Hamlet kills Polonius.
Climax is often described as a point of no return, which, if applied to this play, perfectly fits the events when Polonius was killed. This is the moment when Hamlet committed his first murder, meaning that he would be able to kill Claudius as well when the time comes.