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Math Help - Limits

  1. #1
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    Limits

    Hi how can i factor this limit?

    Find the limit
    \lim_{x \to -1} \frac{2x^2 - x - 3}{x^3+2x^2+6x+5}
    Last edited by ^_^Engineer_Adam^_^; December 7th 2006 at 11:54 PM. Reason: error on latex
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  2. #2
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    I get an error when using latex so

    to factor this limit:

    2x^2 - x - 3 = (2x-3)(x+1)

    x^3 + 2x^2 + 6x + 5 = (x+1)(x^2+x+5)

    the term (x+1) cancels out,and you can compute the limit.
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  3. #3
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    THanks you very much parallel

    how did you factor the denominator?
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  4. #4
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    THanks you very much parallel

    how did you factor the denominator?
    Do you know the Rational Roots Theorem?

    Given a polynomial:
    px^n + ax^{n-1} + ... + bx + q = 0
    If a rational root of this polynomial exists it will be of the form:
    x = \frac{\text{factor of q}}{\text{factor of p}}

    In this case we have:
    x^3 + 2x^2 + 6x + 5

    So if there is a factor of this over the rational numbers it will be of the form:
    (\text{factor of 1}) x - (\text{factor of 5})

    So the possible rational factors of x^3 + 2x^2 + 6x + 5 are:
    (x \pm 1)
    (x \pm 5)

    You can try each of these and find that (x + 1) is the only linear rational factor.

    -Dan
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