Question 732009
you are dividing 4x^2 - 3x + 2 by x

divide 4x^2 by x to get 4x because x * 4x = 4x^2

subtract 4x^2 from 4x^2 - 3x + 2 to get -3x + 2

divide -3x by x to get -3 because -3 * x = -3x

subtract -3x from -3x + 2 to get + 2

since x is a higher order than 2 you are done dividing and 2 is your remainder.

your quotient is 4x - 3 + (2/x)

if you multiply that by x you will get back to 4x^2 - 3x + 2.