Why does it say that Rechav'am strengthened himself?
'Rashi': It is because he was 41 when he became king 1 , so he was able to strengthen himself 2 .
Malbim: It says so above (11:17)! He strengthened himself again (after Shishak came, five years into Rechav'am's kingship), and ruled by himself and ceased to serve Shishak.
'Rashi': This is because he was one year old when Shlomo became king, and Shlomo ruled for 40 years. (Rashi writes that Shlomo was 12 when he became king ? refer to Melachim I, 3:7:2:1. If so, he fathered Rechav'am at the age of 11. We find that minors had children ? Shlomo's great grandfather Achitofel was only 26 years older than Shlomo (Sanhedrin 69b).
Why is 41 a proper age to strengthen himself? Perhaps it is because it is shortly after completing the decade of strength -'Ben Sheloshim l'Ko'ach' (Avos 5:21) (PF).
Why does it mention that Hashem chose to make His name dwell in Yerushalayim?
'Rashi': It is as if the verse complains that through their evil deeds, they caused Hashem's Shechinah to depart from them.
Malbim: The merit of Yerushalayim helped his kingship to last.
