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Math Help - Help with Polynomial and Rational Function

  1. #1
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    Help with Polynomial and Rational Function

    (1) For the function
    h(x) = x3 x2 17x -15,

    use long division to determine which of the following are factors of h(x)

    a) x + 5
    b) x + 1
    c) x + 3

    (2) Determine the oblique asymptote of the graph of the function.

    g(x) = x2 + 4x 1 / x + 3


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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by topsquark View Post
    Oblique asymptotes are almost as easy as their horizontal counterparts.

    As x gets larger and larger the x^2 term in the numerator dominates and the x term in the denominator dominates. So we have:
    \lim_{x \to large} \frac{x^2 + 4x - 1}{x + 3} \to \frac{x^2}{x} = x

    So the oblique asymptote is the line y = x.

    You do the case for when x is large and negative.

    -Dan
    it seems to me that the oblique asymptote is y=x+1 and not y=x..
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  3. #3
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    Quote Originally Posted by kalagota View Post
    it seems to me that the oblique asymptote is y=x+1 and not y=x.
    That is correct. To find the asymptote, you need to do a long division:
    \frac{x^2+4x-1}{x+3} = \frac{(x+3)(x+1)-4}{x+3} = x+1-\frac4{x+3}. As x\to\pm\infty, this approaches x+1.
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  4. #4
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    Here's a good link on polynomial long division: The Remainder Theorem

    You may also want to try synthetic division (the method on the bottom of that page) to check your answer.
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