We need to distinguish from Scripture what changes and what does not change in reference to God.
1) God’s nature does not change. His knowledge, holiness and power neither increase, nor decrease over time.
God is not a man, that He should lie, Nor a son of man, that He should repent; Has He said, and will He not do it? Or has He spoken, and will He not make it good? (Numbers 23:19)
Of old You founded the earth, And the heavens are the work of Your hands. Even they will perish, but You endure; And all of them will wear out like a garment; Like clothing You will change them and they will be changed. But You are the same, And Your years will not come to an end. (Psalm 102:25-27)
For I, the LORD, do not change; therefore you, O sons of Jacob, are not consumed. (Malachi 3:6)
Jesus Christ is the same yesterday and today and forever. (Hebrews 13:8)
This is contradictory to the Mormon conception of God. They believe that God was once as we are, but he has progressed or evolved to become a god. We also may progress to become gods (Doctrine & Covenants 132:19-20 [D & C is one of the Mormon authorities alongside The Book of Mormon]). See also http://en.wikipedia.org/wiki/Mormon_cosmology#cite_note-14
2) Because God’s nature is unchanging, His plans and purposes do not change.
Remember the former things long past, For I am God, and there is no other; I am God, and there is no one like Me, Declaring the end from the beginning, And from ancient times things which have not been done, Saying, “My purpose will be established, And I will accomplish all My good pleasure.” (Isaiah 46:9-10)
The counsel of the LORD stands forever, The plans of His heart from generation to generation. (Psalm 33:11)
In the same way God, desiring even more to show to the heirs of the promise the unchangeableness of His purpose, interposed with an oath, 18 so that by two unchangeable things in which it is impossible for God to lie, we who have taken refuge would have strong encouragement to take hold of the hope set before us. (Hebrews 6:17-18; see vv. 13-20 for context)
Blessed be the God and Father of our Lord Jesus Christ, who has blessed us with every spiritual blessing in the heavenly places in Christ, just as He chose us in Him before the foundation of the world, that we would be holy and blameless before Him. In love He predestined us to adoption as sons through Jesus Christ to Himself, according to the kind intention of His will, to the praise of the glory of His grace, which He freely bestowed on us in the Beloved. (Ephesians 1:3-6 – God’s purpose in election was formed before the foundation of the world)
3) When God is said to repent or to grieve, Scripture is describing the emotional reaction of God to human sin; it is not saying that God has changed His eternal plans and purposes: The LORD was sorry [nacham] that He had made man on the earth (Genesis 6:6). The Hebrew word (nacham) can refer to an emotional response or to a change in mind as we see in an interesting set of verses in 1 Samuel 15.
I regret [nacham] that I have made Saul king (v. 11).
Also the Glory of Israel will not lie or change His mind [nacham]; for He is not a man that He should change His mind [nacham]. (1 Samuel 15:29)
Verse 11 is parallel to Genesis 6:6.
4) Although God does not change, and His eternal plan does not change, He works out His plan for the world in a succession of steps. After the fall, and again after the flood, the human race rapidly deteriorated so that it became like a group of 2-year-olds all throwing temper tantrums at the same time. God began the moral re-education of the race and the spiritual preparation of the world for Christ by making a covenant with Abraham. Later He put a hedge around the nation of Israel and separated it from the surrounding culture by giving the covenant of the Law to Moses. All of this was leading up to Christ (Galatians 3:15-25). God’s final revelation to the world is summed up in Christ (Hebrews 1:1-4—indeed the whole book of Hebrews is about the finality and supremacy of Christ).
The apostles and prophets of the New Testament explained the meaning of Christ’s life, death, resurrection and return. They were instructed by the Holy Spirit to enable them to do this (John 16:12-15; 1 Corinthians 2:6-16). God revealed truth to the apostles; they spoke and wrote it in Spirit guided words; the Christian has the Holy Spirit to help him understand what the apostles wrote. With the passing of that generation of apostles and prophets, new revelation for the whole church ceased. (Of course, God still gives individual guidance, though seldom with any special signs.)
The last Old Testament prophet predicted the arrival of the next prophet, who turned out to be John the Baptist (Malachi 4:5-6; Luke 1:13-17; Matthew 11:7-15). Similarly, the last New Testament prophecy predicted the arrival of the next prophets who will prophesy in the days immediately before Christ’s return (Revelation 11:3-12). So until people see two men who can do the amazing miracles given to these men, they ought not be bamboozled by prophetic claims.
5) Both Muhammad and Joseph Smith claimed to receive revelations from angelic figures. Their revelations are not consistent with the gospel. This is how Scripture evaluates them.
I am amazed that you are so quickly deserting Him who called you by the grace of Christ, for a different gospel; which is really not another; only there are some who are disturbing you, and want to distort the gospel of Christ. But even though we, or an angel from heaven, should preach to you a gospel contrary to that which we have preached to you, let him be accursed. As we have said before, so I say again now, if any man is preaching to you a gospel contrary to that which you received, let him be accursed. (Galatians 1:6-9)
And no wonder, for even Satan disguises himself as an angel of light. (2 Corinthians 11:14)
6) Regarding the Mormon claims that there are many gods:
Scripture sometimes refers to other gods, but these are either empty nothings (Psalm 95:6; 115:4-7) or demons (Deuteronomy 32:17). The gods of the nations are “by nature are no gods” (Galatians 4:8). Scripture is very clear that there is no other god who is worthy of the name.
“You are My witnesses,” declares the LORD, “And My servant whom I have chosen, In order that you may know and believe Me, And understand that I am He. Before Me there was no God formed, And there will be none after Me.” (Isaiah 43:10)
Thus says the LORD, the King of Israel And his Redeemer, the LORD of hosts: 'I am the first and I am the last, And there is no God besides Me. (Isaiah 44:6)
Do not tremble and do not be afraid; Have I not long since announced it to you and declared it? And you are My witnesses. Is there any God besides Me, Or is there any other Rock? I know of none. (Isaiah 44:8)
I am the LORD, and there is no other; Besides Me there is no God. I will gird you, though you have not known Me. (Isaiah 45:5)