A major issue with using the Gospels is that in terms of time Matthew and Luke do not agree as to when Jesus was born.
Matthew specifically puts it 6 to 4 BCE while Luke, with his reference to Quirinius establishes it as being no earlier then 6 CE.
For these reasons, as a primary historical record, the Christian gospels are dubious at best.
For one, the gospels themselves are admittedly propagandist: "And many other signs truly did Jesus in the presence of the disciples, which are not written in this book: but these are written that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have through his name." (John -31) The writers peppered the gospels with Old Testament references — most details of Jesus' life are Old Testament references.
If you want a more historically plausible account of how the Jewish elite would have actually handled the Jesus problem, look at how we’re told they planned to handle the Paul problem (Acts -21).
More likely, they would have killed him immediately upon his vandalism of the temple square, which was guarded by six hundred armed soldiers (with thousands more to summon just a javelin’s throw away in Fort Antonia, which housed a whole Roman legion, adjacent to the Temple: Josephus, Jewish War 2.12.1, 4.5.1, 5.238-248; Jewish Antiquities 20.8.6, 20.8.11), who were not afraid to beat down any rebellious public who got in their way (most especially trouble-makers in the Temple).
When the three synoptic gospels are set side by side, academics are able to work out theories on the relationship between the three texts.
The most generally accepted relationship is that Mark is the earliest text written, and that both Matthew and Luke had a copy of it when writing.
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The gospels are books/collections of writings/scribblings on looseleaf that "document" the birth, life, crucifixion, resurrection, and ascension of Jesus of Nazareth.
Since Paleographic dating as it currently exists is unable "to construct a 95% confidence interval for NT manuscripts without allowing a century for an assigned date" none of the fragments of the canonical Gospels nor non canonal works like Egerton Papyrus 2 can be said definitively predate Against Heresies c. So the best that can be said is that the canonal Gospels existed in some form no later then 145 CE. Of the four canonical gospels, Matthew, Mark, and Luke share similar stories, similar descriptions of events, and even exact phrases from time to time.