Answer:
Hamlet rashly killed the man hiding behind the arras thinking that he was king Claudius. His eagerness to kill his uncle and now king led him to act before he could think properly.
He mourns the incidental death of the "intruding fool" Polonius but decided that he will still work towards achieving his goal of killing Claudius.
Step-by-step explanation:
In Act III of the play "Hamlet" by William Shakespeare, the title character and protagonist Prince Hamlet was in conversation with his mother Queen Gertrude. The initial purpose of this meeting was for the Queen to chastise his son for his rash and unusual behavior of upsetting the king Claudius.
While Hamlet was in conversation with his mother, he found out that someone was hiding behind the curtains. Thinking that it was the King, he drew his sword and killed the man who turns put to be Polonius. His mother exclaims his deed was "rash and bloody". He had thought it was the king but once he knew it was someone else, he felt sorry for the "intruding fool" Polonius and warns his mother that he will wring her heart for her refusal to accept the wrong she had done for her son and dead husband.
His mistaken killing of Polonius did make Hamlet feel regretful but not enough to stop him from finishing his purpose of killing the King Claudius who was responsible for the murder of his own father King Hamlet.