He doesn't, unless it is his plan to annoy her, because that is his main effect on her. Gertrude is a woman of few well-chosen words, and the garrulous and flowery Polonius's method of speaking drives her nuts. "More matter with less art" she brilliantly and tersely chides him.
Polonius is listening to Lord Hamlet's meeting with Gertrude behind the curtain.
Polonius, Ophelia, Gertrude, Hamlet, Claudius, and Laertes.
Hamlet was crazy. She follows Hamlet's instructions and says that "Hamlet hath in madness Polonius slain."
Hamlet thinks Polonius is Claudius. He says, "Is't not the king?" His mistake is reasonable, since Polonius is hiding behind a curtain in Gertrude's bedroom, not the place where one would suspect men other than her husband.
He shows them a love-letter Hamlet wrote to Ophelia.
Polonius tells Claudius and Gertrude that Ophelia and Hamlet have had a relationship which Polonius had Ophelia break off, and that this might be the cause of Hamlet's wild behaviour.
Polonius is listening to Lord Hamlet's meeting with Gertrude behind the curtain.
Polonius, Ophelia, Gertrude, Hamlet, Claudius, and Laertes.
Polonius
No, Gertrude is lying as Hamlet suggested she should.
Hamlet
To eavesdrop on the conversation between Gertrude and Hamlet
Hamlet was crazy. She follows Hamlet's instructions and says that "Hamlet hath in madness Polonius slain."
She said a simple explanation: Hamlet is insane.
Hamlet stabbed him right behind the arras in Queen Gertrude's room.
Gertrude tells Claudius that it was out of madness. This means that Gertrude had not divulged the knowledge that Hamlet was faking his madness.
Polonius, Laertes, Claudius, Rosencrantz, Guildenstern and indirectly Queen Gertrude and Ophelia.