What is the quotient when x^3 -5x^2 + 3x -8 is divided by x-3 ?

For this case we have that the parts of a division are:

Dividend, divisor, quotient and remainder.

To make the division of polynomials, we must build a quotient that when multiplied by the divisor (and when the sign is changed), eliminate the terms of the dividend until reaching the remainder of the division.

It must be fulfilled that:

Then, if we look at the attached figure, the quotient is: