Explain why Laertes and Polonius each warn Ophelia to beware of Hamlet's attentions. What promise does Polonius require from his daughter?

Both Laertes and Polonius believe Hamlet to be playing with Ophelia's affection and warn her accordingly. Laertes also notes that as a prince, Hamlet's marriage will likely be a matter of state. Polonius warn his daughter to guard her virginity and requires a promise that she will behave in an honorable fashion.