A Condemnation of Polygamy in Genesis
First off, the old testament is abundant with polygamy so where is this condemnation stated?
Though it is not explicitly stated, it is indicated either by association to the nature of their character; or the negative consequences of their action when they decide to have another bride. So here is the rationale:
The Tale of Lamech
Genesis 4:23-24 (KJV)
23 And Lamech said unto his wives, Adah and Zillah, Hear my voice; ye wives of Lamech, hearken unto my speech: for I have slain a man to my wounding, and a young man to my hurt.
24 If Cain shall be avenged sevenfold, truly Lamech seventy and sevenfold.
This is the story of the second murder of the bible. Not only that, but this is the first case of polygamy as well. There is very little detail as it's only two verses, but take notice of the second one. Cain was cursed to walk the earth as a vagabond so the Lord (as a condemnation) would deal sevenfold vengeance to whoever slays him. In contrast, Lamech himself guaranteed that he would be avenged seventy sevenfold, and he said it as a boast to his wives. It is also a boast over the Lord as he guarantees his own vengeance to be much greater than that of the Lord's. This is a tale of association. Though his multiple marriages did not cause him to commit murder, an inability to restrain passions will often carry over into acts of violence.
Moreover, his polygamy not only increased violence in the moralistic sense, but in the literal one as well. Meaning his second wife, Zillah, gave birth to a son named Tubal-Cain, who was the inventor of metalsmithing. This means new weapons of warfare such as swords were introduced, being much deadlier than the weapons preceding it. And this only happened because he married a second woman.
*Side note: Notice how he mentions himself in third person, which is usually an indicator that someone lacks good character
Abraham's Marriage to Hagar
Genesis 16:5 (DRA) 5 And Sarai said to Abram: Thou dost unjustly with me: I gave my handmaid into thy bosom, and she perceiving herself to be with child, despiseth me. The Lord judge between me and thee. Sarah (then Sarai) was barren and allowed Abraham (then Abram) to take another wife so he can have an heir. He went through with it and married his Egyption servant Hagar, who would later give birth to Ishmael*. Though this was well-intentioned and Abraham was a righteous man, you can see how quickly it went downhill.
The background being that the Lord promised a great nation to Abraham, and Hagar very likely believed that her son would be an heir to that nation. This gave her a feeling of superiority over Sarah which caused a contentious relationship between the two. Abraham allowed Sarai to deal with Hagar as she wishes, which led to Hagar running away into the desert (though she was later returned after the Lord intervened). Later in Genesis 21 after Sarah gave birth to Isaac, she again casts out Hagar. Her son would have perished had it not been for divine intervention.
These were only the first two explicit examples of polygamy in the bible and you can clearly see the malaise surrounding these two instances. There is a misconception where polygamy is condoned in the old testament, but that is incorrect as the Lord could not hold back man's sinful nature even with severe punishment being applied (A prime example being the tower of Babel being built so soon after the great flood). Therefore, the Lord had to be more accommodating due to the hardness of our hearts.
Note: Don't mind my switching between the King James and Douay-Rheims versions of the bible. I'll often use the King James because many spellings and pronunciations of names stem from this version. In other cases, I feel like the DRA conveys the message better than the other. I mainly use these older versions because I love the language. I don't object to newer editions, it is merely a personal preference