Just at this time some actors came to the Court, and Hamlet ordered them to perform a certain play before the King and Queen. Now, this play was the story of a man who had been murdered in his garden by a near relation, who afterwards married the dead man's wife. You may imagine the feelings of the wicked King, as he sat on his throne, with the Queen beside him and all his Court around, and saw, acted on the stage, the very wickedness that he had himself done. And when, in the play, the wicked relation poured poison into the ear of the sleeping man, the wicked Claudius suddenly rose, and staggered from the room—the Queen and others following. Then said Hamlet to his friends— "Now I am sure the ghost spoke true. For if Claudius had not done this murder, he could not have been so distressed to see it in a play." Now the Queen sent for Hamlet, by the King's desire, to scold him for his conduct during the play, and for other matters; and Claudius, wishing to know exactly what happened, told old Polonius to hide himself behind the hangings in the Queen's room. And as they talked, the Queen got frightened at Hamlet's rough, strange words, and cried for help, and Polonius behind the curtain cried out too. Hamlet, thinking it was the King who was hidden there, thrust with his sword at the hangings, and killed, not the King, but poor old Polonius. So now Hamlet had offended his uncle and his mother, and by bad hap killed his true love's father. "Oh! what a rash and bloody deed is this," cried the Queen. And Hamlet answered bitterly, "Almost as bad as to kill a king, and marry his brother." Then Hamlet told the Queen plainly all his thoughts and how he knew of the murder, and begged her, at least, to have no more friendship or kindness of the base Claudius, who had killed the good King. And as they spoke the King's ghost again appeared before Hamlet, but the Queen could not see it. So when the ghost had gone, they parted.

What is the purpose in having Hamlet kill Polonius?

It allows the ghost of the King to appear again.
It sets the King and Queen against Hamlet.
It shows that Hamlet does not care who he kills.
It indicates that Polonius is actually the murderer.