Notas del episodio
In dealing with this question, we examine several other texts: Genesis 6:6-7, Exodus 32:14, and Jonah 3:10 which all demonstrate similar activity of relenting from God.
In contrast we examined Numbers 23:19, Malachi 3:6, and most especially within the same chapter as the question, 1 Samuel 15:29. It is clear that both the immediate context of 1 Samuel 15 as well as the greater teaching of all of Scripture is that God does not change His mind.
We examined more carefully the difference between God changing His mind, which He does not do, and with Him feeling sorrow over the consequences of what had happened. Even in Genesis 6 with God feeling sorry for making man, He continued on with the process that was originally started. He did not wipe man out completely, but He preserved Noah and His family. He didn't make a new creation, He kept going with the original plan.
We spend time fleshing out the emotional nature of God in relation to sin and disobedience in contrast to God's fixed and eternal plan which does not change. Please make sure to ask any follow-up questions if there are still areas of confusion in regard to this question.