(3x^3+4x^2-7x+6) / (x-3)
quotient and remainder
hard to show long algebraic division on this forum,
I hope you are familiar with synthetic division
It will look something like this
3 | 3 4 -7 6
........9 39 84
... 3 13 32 102
so
(3x^3+4x^2-7x+6) / (x-3) = (3x^2 + 13x + 32) + 102/(x-3)