Polygamy is the process where a man marries more than one wife. Polygamy has been in existence for long, some men like Abraham and Solomon in the bible married many wives. God does not fully approve it but he didn't stop those men from marrying more than one wife. Polygamy brings jealousy and hate among the women in the family, it shows that God never approves of polygamy.
From the beginning of this life who have always wanted one man to marry one woman. In the book of genesis God only created one woman for Adam to be his wife. In the new testament Jesus also taught that a man should leave his parents and get married to a woman. This is a clear picture that God accepts monogamy not polygamy since the beginning of this life.