DOES ISLAM PROMOTE POLYGAMY?

No, polygamy in Islam is a permission not an injunction.
Historically, all the prophets except Jesus, who was not married, had more than one wife. For Muslim men to have more than one wife is a permission which is given to them in the Quran, not to satisfy lust, but for the welfare of the widows and the orphans of the wars.

In the pre-Islamic period, men used to have many wives. One person had 11 wives and when he became Muslim, he asked the Prophet Muhammad (P), “What should I do with so many wives?” and he said, “Divorce all except the four.” The Quran says, “you can marry 2 or 3 and up to 4 women if you can be equally just with each of them” (4:3).
Since it is very difficult to be equally just with all wives, in practice, most of the Muslim men do not have more than one wife. Prophet Muhammad (P) himself from age 24 to 50 was married to only one woman, Khadija.

In the western society, some men who have one wife have many extramarital affairs. Thus, a survey was published in “U.S.A. Today” (April 4, 1988 Section D) which asked 4,700 mistresses what they would like their status to be. They said that “they preferred being a second wife rather than the ‘other woman’ because they did not have the legal rights, nor did they have the financial equality of the legally married wives, and it appeared that they were being used by these men.”