Let's do the long division
#color(white)(aaaa)##6x^4-8x^3+14x^2-x-1##color(white)(aaaa)##∣##3x-1#
#color(white)(aaaa)##6x^4-2x^3##color(white)(aaaaaaaaaaaaaaaaa)##∣##2x^3-2x^2+4x+1#
#color(white)(aaaaaa)##0-6x^3+14x^2#
#color(white)(aaaaaaaa)##-6x^3+2x^2#
#color(white)(aaaaaaaaaaa)##0+12x^2-x#
#color(white)(aaaaaaaaaaaaa)##+12x^2-4x#
#color(white)(aaaaaaaaaaaaaaaaa)##0+3x-1#
#color(white)(aaaaaaaaaaaaaaaaaaa)##+3x-1#
#color(white)(aaaaaaaaaaaaaaaaaaaa)##+0-0#
The remainder is #0# and the quotient is #=2x^3-2x^2+4x+1#
