SARAH:  Polonius realizes his earlier mistake about Hamlet; he also seems to realize that it was his own overly suspicious nature that led him astray.

RALPH:  We'll have to see as the play continues whether or not Polonius has learned anything from this mistake.

SARAH:  But Ralph, Polonius's last two lines are a bit difficult to untangle. "This must be known..."

RALPH:  This must be told to the King — The apparent reason for the Hamlet's madness must be told to the king...

SARAH:  "which being kept close, might move more grief to hide..."

RALPH:  which if we kept it a secret, it might cause more problems by remaining unknown...

SARAH:  "than hate to utter love."

RALPH:  than the anger of the king when we tell him of the love affair.

SARAH:  The idea here is that Polonius thinks that the King will be angry to hear about Ophelia and Hamlet's relationship, but it will be better to tell him than to keep it from him.

RALPH:  Polonius apparently assumes here that King Claudius, and perhaps Gertrude as well, would frown upon a love affair between Hamlet and Ophelia, as Ophelia would not be a proper match for the young prince.

SARAH:  But it's not clear that the King and Queen would see things this way — here's another example of Polonius quickly jumping to conclusions.