Given: (x^3-7x-6)/(x+1)x3−7x−6x+1
color(Blue)("Different format but still the traditional long division method.")Different format but still the traditional long division method.
Using place keepers of zero value. Example: 0x^20x2
color(white)("ddddddddddd")x^3+0x^2-7x-6dddddddddddx3+0x2−7x−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)
