Expert: Richard J. Raridon - 2/8/2005

Question
(x^3-1)/(x-1)
I know the answer is x^2 +x +1,however I don't understand how to get that.
One reason is:
when my teacher did this problem on the board, he told us to go like regular long-division and he said to do x into x^3     (ie. x^3/x). My question is what happened to using the -1?That's one of my many problems on this.
I know somewhere along the line I'm missing a point.
Can you please help me.Thanks

Answer
Your teacher was right.  You can do it like regular long division.  x into x^3 gives you x^2
so you multiply x^2 by x-1 and you get x^3-x^2
subtract that from x^3  and you get x^2
so now you have x^2/x which gives you the 2nd term, x
multiply x by x-1 and you get x^2-x
subtract that from x^2 and you have x.
x/x gives you 1
multiply that by x-1 and you have x-1
so subtract that from the x and include the -1
and you have no remainder
so (x^3-1)/(x-1) = x^2 +x +1
I'll write it out (ignore the *'s)
***********x^2+x+1
***********__________
*******x-1|x^3*****-1
***********x^3-x^2
***********_______
***************x^2
***************x^2-x
***************______
*******************x
*******************x-1
*******************_____
*********************0
Does that help?