For some reason, there are many who feel that, because the Bible mentions things like polygamy, slavery, and child labor that the Bible promotes those ideas. This is untrue. Just because the Bible mentions something does not necessarily mean that the Bible is supporting such a thing. One of the major gripes that some people have with the Bible is that they feel the mentions of polygamy or other types of odd marriage relationships, serve to be God's endorsement. This is untrue, and one's understanding of the full context of the Bible proves such.
In Genesis 25:1-11 the Bible mentions that Abraham had other wives besides Sarah. The scriptures identify that Abraham lived to be 175 years old. Sarah died when she was 127 years old, which means that she died when Abraham was 137. Thus, Abraham lived 38 more years after Sarah. While the scriptures are not clear as to when Abraham took up this new wife, it is clear that she likely came into the picture towards the later part of Abraham's life, and possibly right before Sarah died.
Some suppose that since Abraham had concubines, that God approved of Abraham's choices. This is not necessarily true. Recall that when God made Adam and Eve, He desired for husband and wife to be joined together as one. There was no provision for other women because polygamous relationships were not the will of God. Thus, when one examines polygamous relationships in the Bible, one will find that there is always miserable consequences that play out, though God's specific displeasure may not necessarily be mentioned. The Bible usually describes God displaying His mercy and grace to restore the relationships that people find a way to destroy. For example, when Abraham took Hagar as a concubine, God did not specifically state His displeasure with Abraham and Sarah, but was stern to state that Ishmael would not be the heir of Abraham, and was gracious to provide for Hagar and Ishmael when they were kicked out of Abraham's household into the wilderness.
Genesis 25:1-11 explains that Abraham took another wife named Keturah. Though God does not demonstrate His displeasure with this relationship, the fruit of this relationship proves itself to be problematic as time progressed. Though the scriptures are not necessarily against remarriage, one must be careful in how one's decisions flow within the will of God. Understanding this truth, one must take into account God's will as historically explained in the Bible, compared to Abraham's decision to take on another wife. God wanted husband and wife to become as one. God wanted Isaac to be the heir of Abraham to inherit the promises that God made in Genesis chapter 12. Abraham decided to take on another wife, and then had 6 other children with her.
This decision eventually caused problems. Since Abraham was obedient to God's will to give all of his possessions to Isaac as the heir of God's promises, there were 6 other children (7 including Ishmael), whose father was Abraham, that didn't get quite as much. Over time, this would create jealousy, so that the children of Abraham that are mentioned by name, would eventually birth people groups that historically caused problems for the children of Israel. Where Isaac received the inheritance and blessing of his father, the other children received "gifts," which were far less in value and were sent off to live in other lands. These dynamics created division within the family of Abraham so that nations such as Midian, Sheba and Dedan would be disruptive to the peace of Israel.
Though it is debatable whether or not Abraham should have remarried, one must wonder if he took God's will for Isaac into account when his decision was made to extend his family. God's plan for Abraham was unique and thoroughly stated. Abraham had learned in his old age to trust in God's will and promises. However, one can see that not every decision that Abraham made facilitated the peaceful fulfillment of God's promises. While God did not vocally express His opinion regarding Abraham's multiple marriages and family extensions, Jewish history shows that God did not bless these relationships over time. These relationships caused chaos and grief for the descendants of Isaac.
In the end, Abraham died at 175 years old and would never physically see the affects of his decisions. Nevertheless, history, Biblical or otherwise, shows that this family had its fair share of issues. Though the Bible does not specifically state God's opinion on the matter, Abraham didn't seem to consider how his actions would affect the will of God for Isaac. This is not to suggest that God is against remarriage (though polygamy is always out of the question), but does show that one must consider how one's decisions affect God's plan and will, lest the consequences become chaotic.