How do they gladden the king?
Rashi: He desires the evil that they do.
Radak #1: When they consented to Yaravam about the calves, they gladdened him.
Radak #2: Every day they gladden their king via their oppression and extortion, for his hand is with them.
Malbim: The Navi begins to tell how they fell via Melech Ashur, who exiled them from their land. The first reason was that they rebelled against their kings and killed them 1 ? Afterwards, Hoshe'a ben Elah killed Pekach and ruled in place of him. Shalman'eser Melech Ashur came, and Hoshe'a was a slave to him. Shalman'eser found 2 that Hoshe'a sent to Soa Melech Mitzrayim, so he incarcerated Hoshe'a, besieged Shomron and exiled Yisrael to Ashur. Here it says that initially, when they were faithful to their king, and he rejoiced in their evil, they strove to gladden him.
Malbim: First they killed Zecharyah ben Yaravam ? "va'Yikshor Alav Shalum ben Yavesh va'Yakehu Kabal Am" (Melachim II, 15:10). Menachem ben Gadi killed Shalum and ruled in place of him. This caused that Pul Melech Ashur came to the land, and Menachem gave to him 1,000 Kikarim of silver to solidify his kingship (Melachim II, 15:19). Afterwards Pekach ben Remalyahu killed Pekachiyah ben Menachem and ruled in place of him. Tiglas Pil'eser Melech Ashur came against him and exiled Zevulun and Naftoli; this was via Achaz.
Malbim: Shalman'eser found out via informers in Bnei Yisrael. They rebelled against Hoshe'a and plotted to destroy him. The Nevu'os until the end of the Sefer refer to these matters.
What do we learn from "uv'Chachasheihem Sarim"?
Radak #1: When they denied Hashem and said "Hine 1 Elohecha Yisrael" (Melachim I, 12:28), also the officers who agreed with Yaravam rejoiced in that counsel.
Radak #2: When they deny and lie to each other, the officers rejoice, for also they support their hands.
We changed the text, for "Eleh Elohecha Yisrael" (Shemos 32:8) was said in the Midbar, more than 500 years before Yaravam made calves. (PF)
