How do you find the quotient of #(6x^3+16x^2-60x+39)div(2x+10)#?

We can perform either a long division or a synthetic division

Let #f(x)=6x^3+16x^2-60x+39#

Let's perform the synthetic division

#color(white)(aaaa)##-5##color(white)(aaaaa)##|##color(white)(aaaa)##6##color(white)(aaaaaa)##16##color(white)(aaaaa)##-60##color(white)(aaaaa)##39#
#color(white)(aaaaaaaaaaaa)#_________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##color(white)(aaaaaa)##-30##color(white)(aaaaaa)##70##color(white)(aaaaa)##-50#
#color(white)(aaaaaaaaaaaa)#________

#color(white)(aaaa)##color(white)(aaaaaaa)##|##color(white)(aaaa)##6##color(white)(aaaaaa)##-14##color(white)(aaaaaa)##10##color(white)(aaaa)##color(red)(-11)#

#f(x)=(6x^2-14x+10)-11/(x+5)#

or

#f(x)=3x^2-7x+5-11/(2x+10)#

The remainder is #=-11#

# color(white)(...............................)color(blue)(3x^2-7x+5#
#color(white)(a)2x+10##|## color(white)(.)overline(6x^3+16x^2-60x+39#
#color(white)(...................)ul(6x^3+30x^2)#
#color(white)(.........................)-14x^2-60x#
#color(white)(...........................)ul(-14x^2-70x)#
#color(white)(.........................................)10x+39#
#color(white)(..........................................)ul(10x+50)#
#color(white)(..............................................)0-11#