(-6x^4-3x^3-2x^2-4x-7)/(x^2+3)
The Long Division method:
" " " " " " " " " " " "underline(-6x^2-3x+16" " " " " " " " " " " " " " " " " " ")
x^2+0*x+3|~-6x^4-3x^3-2x^2-4x-7
" " " " " " " " " " " "underline(-6x^4+0*x^3-18x^2" " " " " ")
" " " " " " " " " " " " " " " " "-3x^3+16x^2-4x-7
" " " " " " " " " " " " " " " " "underline(-3x^3+0*x^2-9x)
" " " " " " " " " " " " " " " " " " " " " "16x^2+5x-7
" " " " " " " " " " " " " " " " " " " " " "underline(16x^2+0*x+48)
" " " " " " " " " " " " " " " " " " " " " " " " " "+5x-55 larrRemainder
The answer
color(blue)((-6x^4-3x^3-2x^2-4x-7)/(x^2+3)=-6x^2-3x+16+(5x-55)/(x^2+3))