The Quran prohibits Muslim men from marrying unbelievers and associators, saying that it is better for them to marry believing women:

And do not marry the idolatresses until they believe, and certainly a believing maid is better than an idolatress woman, even though she should please you; and do not give (believing women) in marriage to idolaters until they believe, and certainly a believing servant is better than an idolater, even though he should please you; these invite to the fire, and Allah invites to the garden and to forgiveness by His will, and makes clear His communications to men, that they may be mindful. S. 2:221 Shakir

The words rendered as idolatresses and idolaters are from the Arabic term mushrik, which comes from shirk, and more literally means one who associates or ascribes partners to Allah. This is how the late Muhammad Asad translated these words:

AND DO NOT many women who ascribe divinity to aught beside God ere they attain to [true] belief: for any believing bondwoman [of God] is certainly better than a woman who ascribes divinity to aught beside God, even though she please you greatly. And do not give your women in marriage to men who ascribe divinity to aught beside God ere they attain to [true] belief: for- any believing bondman [of God] is certainly better than a man who ascribes divinity to aught beside God, even though he please you greatly. [Such as] these invite unto the fire, whereas God invites unto paradise, and unto [the achievement of] forgiveness by His leave; and He makes clear His messages unto mankind, so that they might bear them in mind. Muhammad Asad

In fact, true believers according to the Muslim scripture are only those who believe in Allah and Muhammad as his messenger:

The true believers are ONLY those, who believe in (the Oneness of) Allah and His Messenger (Muhammad), and when they are with him on some common matter, they go not away until they have asked his permission. Verily! Those who ask your permission, those are they who (really) believe in Allah and His Messenger. So if they ask your permission for some affairs of theirs, give permission to whom you will of them, and ask Allah for their forgiveness. Truly, Allah is Oft-Forgiving, Most Merciful. S. 24:62 Hilali-Khan

The next text commands Muslim men not to remain married to unbelievers:

O you who believe! when believing women come to you flying, then examine them; Allah knows best their faith; then if you find them to be believing women, do not send them back to the unbelievers, neither are these (women) lawful for them, nor are those (men) lawful for them, and give them what they have spent; and no blame attaches to you in marrying them when you give them their dowries; and hold not to the ties of marriage of unbelieving women, and ask for what you have spent, and let them ask for what they have spent. That is Allah's judgment; He judges between you, and Allah is Knowing, Wise. S. 60:10 Shakir

The word for unbeliever comes from the term kafir, which refers to one who makes kufr. According to the Quran, the Jews and Christians (specifically the latter) fall under these categories of mushrik and kafir:

O ye who believe! surely, the idolaters are unclean (al-mushrikoona najasun). So they shall not approach the Sacred Mosque after this year of theirs. And if you fear poverty, ALLAH will enrich you out of HIS bounty, if HE pleases. Surely, ALLAH is All-Knowing, Wise. Fight those from among the people of the Book, who believe not in ALLAH, nor in the Last Day, nor hold as unlawful what ALLAH and HIS Messenger have declared to be unlawful, nor follow the true religion, until they pay the tax considering it a favour and acknowledge their subjection. And the Jews say, ‘Ezra is the son of ALLAH,’ and the Christians say, ‘the Messiah is the son of ALLAH;’ that is what they say with their mouths. They only imitate the saying of those who disbelieved (kafaroo) before them. ALLAH's curse be on them! How they are turned away. They have taken their priest and their monks for lords besides ALLAH. And so have they taken the Messiah, son of Mary. And they were not commanded but to worship the One God. There is no God but HE. Holy is HE far above what they associate (yushrikoona) with Him! They seek to extinguish the light of ALLAH with their mouths; but ALLAH refuses but to perfect HIS light, though the disbelievers (al-kafiroona) may resent it. HE it is Who has sent HIS Messenger with guidance and the religion of truth, that HE may make it prevail over every other religion, even though the idolaters (al-mushrikoona) may resent it. S. 9:28-33 Sher Ali

The above passage claims that not only are Christians idolaters (or of those who associate partners with God) and blasphemers (or disbelievers), but the Jews are as well. It even classifies the Jews and Christians as unclean!

They indeed have disbelieved (kafara) who say, `Surely ALLAH - He is the Messiah, son of Mary.' Say, `Who then has any power against ALLAH, if HE desired to destroy the Messiah, son of Mary, and his mother and all those that are in the earth?' And to ALLAH belongs the Kingdom of the heavens and the earth and what is between them. HE creates what HE pleases and ALLAH has power over all things. S. 5:17 Sher Ali

They are unbelievers (kafara) who say, 'God is the Messiah, Mary's son.' For the Messiah said, 'Children of Israel, serve God, my Lord and your Lord. Verily whoso associates with God anything (innahu man yushrik biAllahi), God shall prohibit him entrance to Paradise, and his refuge shall be the Fire; and wrongdoers shall have no helpers.' S. 5:72 Arberry

Certainly they disbelieve (kafara) who say: Surely Allah is the third (person) of the three; and there is no god but the one God, and if they desist not from what they say, a painful chastisement shall befall those among them who disbelieve. S. 5:73 Shakir

The following sahih hadith confirms the view that Christians are both mushriks and kafirs:

Narrated Nafi’:
Whenever Ibn ‘Umar was asked about marrying a Christian lady or a Jewess, he would say: "Allah has made it unlawful for the believers to marry ladies who ascribe partners in worship to Allah, and I do not know of a greater thing, as regards to ascribing partners in worship, etc. to Allah, than that a lady should say that Jesus is her Lord although he is just one of Allah's slaves." (Sahih al-Bukhari, Volume 7, Book 63, Number 209)

This online Salafi site unapologetically calls Christians kafirs and says that:

This is something that is well known among the Muslims, and they are UNANIMOUSLY AGREED that the Christians are kaafirs, and even that those who do not regard them as kaafirs ARE ALSO KAAFIRS. Shaykh Muhammad ibn 'Abd al-Wahhaab said concerning the things which are unanimously agreed to nullify Islam:

"Whoever does not regard the mushrikoon as kaafirs, or doubts that they are kaafirs, or thinks their religion is correct, is himself a kaafir." ... (Question #12713: Is the trinity that the Christians believe in mentioned in Islam?; underline and capital emphasis ours)

Yet the following verse says that Muslim men can marry women who are Jews and Christians!

Today the good things are permitted you, and the food of those who were given the Book is permitted to you, and permitted to them is your food; Likewise believing women in wedlock, and in wedlock women of them who were given the Book before you if you give them their wages, in wedlock and not in licence, or as taking lovers. Whoso disbelieves in the faith, his work has failed, and in the world to come he shall be among the losers. S. 5:5 Arberry

No true book of God would contradict itself like this. Hence, based on the confusion in the above passages the Quran definitely cannot be from God.

Further Reading

The Quranic View of Christians - Fellow Believers or Unbelieving Polytheists?
Thoughts on Marriages between Muslims and Christians

Contradictions in the Qur'an
Answering Islam Home Page