Expert: Ahmed Salami - 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
Hi,
Please forgive the delay.I'm on vacation.
I'll just take it from where you stopped.
After getting x^2(i.e x^3/x), multiply by x-1 to get
x^3 - x^2. Substract this from x^3 - 1 to get x^2 - 1. Divide again and continue in this way until you end up with zero after substraction and i'm sure you'll be fine.
I'm not on duty but i'll let you contact me on sa_ahmed2001@yahoo.com as a privilege.
I hope you get it.
Regards.