Given: #(x^3-7x-6)/(x+1)#
#color(Blue)("Different format but still the traditional long division method.")#
Using place keepers of zero value. Example: #0x^2#
#color(white)("ddddddddddd")x^3+0x^2-7x-6#
#color(magenta)(x^2)(x+1)->ul(2x^3+x^2larr" Subtract")#
#color(white)("ddddddddddd.d")0-x^2-7x-6#
#color(magenta)(-x)(x+1)->color(white)("ddd")ul(-x^2-x larr" Subtract")#
#color(white)("dddddddddddddddd")0 color(white)("d")-6x-6#
#color(magenta)(-6)(x+1)->color(white)("dddddd.d")ul(-6x-6larr" Subtract")#
#color(white)("ddddddddddddddddddddd")0+0#
#color(magenta)(x^2-x-6)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Synthetic division method.")#
Consider the denominator of #x+1=0 => x=color(red)(-1)#
#x^3+0x^2-7x-6 #
#color(green)(1 color(white)("..")+0color(white)("d.")-7color(white)("d")-6)#
#color(white)("dddd")color(red)(-1) | color(white)("d")color(green)(1+0-7-6) #
#color(white)("ddddd..d")ul(|color(white)(".")darr -1+1+6" " #
#color(white)("ddddddddd")1color(white)("d")-1 -6 +0#
#color(white)("ddddddd.d")darrcolor(white)("dd")darrcolor(white)("d")darr#
#color(white)("dddddddd")1x^2-1x-6#
#color(magenta)(color(white)("ddddddddd")x^2-color(white)("d")x-6)#
