The Qur'an doesn't say that the Bible is the word of God. Muslims believe the Bible is just a book written by various men over a period of many years. The Qur'an mentions the Injil/Gospel of Jesus (Not the four gospels found in the Bible), the Zabur/Psalms of David, the Tawrat/Torah of Moses, and the Suhuf/Scrolls of Abraham as being direct revelations from God, but most Muslims believe that they no longer exist today in their original form.
He sent down to you the Book with the Truth [The Qur'an],
confirming what came before it [The Injil, the Zabur, the Tawrat, and the Suhuf];
and He sent down the Torah and the Gospel [The Injil, Not the Gospels of Matthew, John, Luke, and Mark]. (Qur'an 3:3)
The "People of the Book" are considered those nations/people who received previous revelations from God through the prophets. The "Book" isn't the Bible, but rather the Book that is in the presence of God known as the Mother of Books. It's from this Mother of Books that the Injil/Gospel of Jesus, the Zabur/Psalms of David, the Tawrat/Torah of Moses, and the Suhuf/Scrolls of Abraham originated from. They are individual books/scriptures, and not contained in a single book like our Bible. The Qur'an also originated from the Mother of Books.
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