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Limit question

  1. Feb 17, 2006 #1
    Here is the question,
    Evaluate this limit:
    [tex]\lim_{x\rightarrow 1} \frac{x^3-1}{x^2-1}[/tex]
    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. jcsd
  3. Feb 17, 2006 #2
    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.
  4. Feb 18, 2006 #3


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    Science Advisor

    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).
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