Trifling question about Polonius, R&G

[Miss Plum]

Act II, scene 2, line 210 --

Polonius: You go to seek the Lord Hamlet. There he is.


Why does Polonius usher Rosencrantz and Guildenstern in to Hamlet? Why don't they enter unassisted, or guided by some unnamed Attendant? How does Polonius know that R&G are looking for Hamlet? Pol wasn't present when Gertrude and Claudius received R&G.

Also, would he be jealous of the R&G scheme? He wants to advance himself by being the one to discover the cause of Hamlet's odd behavior, but they're on the case, too. Maybe that's why he amped up his efforts and hid behind the arras in Gertrude's room?

[Charles Darnay]

Polonius does not usher them in, he is on stage when they enter. The line you refer to is no more than a theatrical device to get them in the scene

[Miss Plum]

Oh dear, thank you. That's what I get for taking every letter and comma of this play as a deep message.