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Math Help - long division with a trinomial

  1. #1
    Junior Member
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    long division with a trinomial

    [2x^(3)-4x-15x+5] / [x-2x-8]

    i get 2x with a remainder of x+5...is this right or did i do this wrong?
    if it's right how do i write this properly
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  2. #2
    A Plied Mathematician
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    You're correct. The proper way to write your result is as follows:

    2x+\dfrac{x+5}{x^{2}-2x-8}.

    Incidentally, you can check your own work by getting a common denominator and adding the two fractions together like this:

    2x+\dfrac{x+5}{x^{2}-2x-8}=\dfrac{2x}{1}+\dfrac{x+5}{x^{2}-2x-8}=\dfrac{2x(x^{2}-2x-8)}{x^{2}-2x-8}+\dfrac{x+5}{x^{2}-2x-8}\dots

    You should get back to the original fraction.
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