Question 332271
Use polynomial long division to get 



<img src="http://i150.photobucket.com/albums/s91/jim_thompson5910/Algebra%20dot%20com/gifs42w214h176.gif">



So {{{(4x^3+6x^2-2x+3)/(2x-1)}}} equals {{{2x^2+4x+1}}} remainder 4



Put another way, {{{(4x^3+6x^2-2x+3)/(2x-1)=2x^2+4x+1+4/(2x-1)}}}