Question

How do you divide `(x^3 - 7x - 6 )` by `x+1`?

Answer 1

`(x^3-7x-6)div(x+1) = x^2-x-6` (with a remainder of `0`)
This could be done by long polynomial division or synthetic division.

Explanation:

Using synthetic division to divide `color(brown)(1)x^3color(brown)(+0)x^2color(brown)(-7)xcolor(brown)(-6)` by `(x- (color(cyan)(-1)))`

#{: (,,x^3,x^2,x^1,x^0), (,"|",color(brown)(1),color(brown)(+0),color(brown)(-7),color(brown)(-6)), (,"|",,-1,1,6), ("-----","|","------","------","------","------"), (xx color(cyan)((-1)),"|",color(red)(1),color(red)(-1),color(red)(-6),color(blue)(0)), (,,x^2,x^1,x^0,color(blue)("Remainder")) :}#

Notre: the top and bottom rows of this table are only helpful reminders; they are not usually included in a synthetic division.