What will David teach to Posh'im?
Rashi: If they see that You pardon me, they will learn from me to repent. Radak - I will teach to them that you are "Nosei Avon va'Fesha" (Shemos 34:7), and they will repent, and You will accept them. Sha'arei Teshuvah (1:42) - returning the masses from sin, as much as possible, is one of the primary aspects of Teshuvah.
Malbim: Posh'im sin to rebel, not due to desire. Most of them think that Hashem's ways are not good. I will teach to them Your ways, that they are good, and they will repent.
Why will the Chata'im repent?
Malbim: They sin due to desire, and not due to lack of knowledge. They need not be taught. They will see that I overpower my desire and I repented, even though my nature leaned towards desire, also they will overcome their desire and repent. They will see that you have mercy and judge righteously. This corresponds to "v'Ru'ach Kodshecha Al Tikach Mimeni" - with the help of the Ru'ach Nedivah, i.e. Ru'ach ha'Kodesh.
It says "v'Chata'im" here, and above ("v'Chata'im ba'Adas Tzadikim" - 1:5). What is the significance of this?
Ba'al ha'Turim: This teaches that if sinners repent, they will stand in Adas Tzadikim.
