# Limit question

1. Feb 17, 2006

### fstam2

Here is the question,
Evaluate this limit:
$$\lim_{x\rightarrow 1} \frac{x^3-1}{x^2-1}$$
since there is no common factor, this limit does not exist, correct?
Maybe I am missing a basic algebra rule for the numerator to find a common factor.
Thank you.

Last edited: Feb 17, 2006
2. Feb 17, 2006

### dicerandom

You can factor an (x-1) out of the numerator. You can see that this must be so since x=1 is a root of x^3-1 and a polynomial must factor out into its roots. You can use synthetic division to find what the other factor should be.

3. Feb 18, 2006

### HallsofIvy

Staff Emeritus
There is no common factor?? If p(1)= 0 for any polynomial p then (x-1) must be a common factor!! x3-1= (x-1)(x2+ x+ 1) and x2- 1= (x-1)(x+ 1).