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

1 Answer
Oct 29, 2015

#(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.