What is the scriptural basis for that?
I'll start with what is on the Church's web page:
Question:
What is the Church’s position on polygamy?
Answer:
In 1998, President Gordon B. Hinckley made the following statement about the Church's position on plural marriage: "This Church has nothing whatever to do with those practicing polygamy. They are not members of this Church . . . If any of our members are found to be practicing plural marriage, they are excommunicated, the most serious penalty the Church can impose. Not only are those so involved in direct violation of the civil law, they are in violation of the law of this Church."
At various times, the Lord has commanded His people to practice plural marriage. For example, He gave this command to Abraham, Isaac, Jacob, Moses, David, and Solomon (Doctrine and Covenants 132:1).
In this dispensation, the Lord commanded some of the early Saints to practice plural marriage. The Prophet Joseph Smith and those closest to him, including Brigham Young and Heber C. Kimball, were challenged by this command, but they obeyed it. Church leaders regulated the practice. Those entering into it had to be authorized to do so, and the marriages had to be performed through the sealing power of the priesthood. In 1890, President Wilford Woodruff received a revelation that the leaders of the Church should cease teaching the practice of plural marriage (Official Declaration 1).
Here are my comments on this.
We believe that we are a "restoration" gospel. This means that we believe that there has been at least one falling away, or apostasy, from the true gospel.
We believe that the true gospel was restored (through Joseph Smith). This pretty much defines how we are different from other Christian faiths. We believe that some truths were lost (or fallen away) and have now been restored.
One of the concepts of a restoration is that all truths will be restored. This includes law and practices. This includes polygamy.
It would appear that in the Old Testament some prophets were given the law of polygamy. Abraham comes to mind (Gen 16:1-11). Jacob also (Gen 29:28).
Exodus 21:10 seems to set some requirements for it. Deut 21:15 also. Deut 17:17 implies that kings should not "multiply" wives, so polygamy doesn't appear to apply to everybody. David seems to have many wives (2 Sam 5:13), yet Nathan seems to only condemn him for taking Uriah's wife (2 Sam 12:7-9), and it seems only because he killed to do it.
In 1 Kings 11:1-4, Solomon seem to be chastised, not for taking many wives, but for taking "strange" wives from other faiths that turned him away from the Lord.
Isaiah 4:1 would seem to suggest that in the millennium "seven women shall take hold of one man" and be "called by [his] name." Maybe there will be a shortage of men in the millennium (see my comments in an earlier post).
There are a few other scriptures. Some seem to condemn polygamy, others seem neutral on it. If we claim that we are a restoration Gospel, then we must have a restoration of all laws and truths. If polygamy was a law, then it must be restored. That pretty much is it.
Hope this helps to answer. I know it is long.