Divide using synthetic division. (6x^5-4x^3+3x^2-2x+3) ÷ (x-2)=

2..|..6...0...-4...3...-2...3
.........12...24..40..86..168
....-------------------------------
......6..12..20..43..84..171

So, (6x^5-4x^3+3x^2-2x+3) ÷ (x-2) = (6x^4 + 12x^3 + 20x^2 + 43x + 84) + 171/(x - 2).

I hope this helps!

6x^5+ 0x^4 -4x^3+3x^2-2x+3 | x-2
________________________ __________________________
6x^5 + 0x^4 ______________| 6x^4 + 12x^3 + 20x² + 43x + 84
6x^5 - 12x^4 _____________|
____ 12x^4 - 4x^3 _________|
____ 12x^4 - 24x^3 _______|
__________ 20x^3+3x² ____|
__________ 20x^3-40x² ____|
_______________ 43x² - 2x _|
_______________ 43x² -86x _|
_______ ____________ 84x+3|
_______ ____________ 84x-168|
_______ ________________ -165