Limit Evaluation: Does $\lim_{x\rightarrow 1} \frac{x^3-1}{x^2-1}$ Exist?

[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.

 

[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.

 

[HallsofIvy]

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).