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Partial Fractions

  1. Jun 26, 2009 #1

    Mentallic

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    I'm having trouble understanding what the numerator needs to be in the partial fractions.
    e.g.

    [tex]\frac{1}{(x-1)(x-2)^2}\equiv \frac{A}{x-1}+\frac{Bx+C}{(x-2)^2}[/tex]

    Notice how the first numerator has a constant A, while the second is linear Bx+C.
    Actually... just now I think I may understand it. Does it have to do with the fact that during synthetic division, the remainder is always 1 degree less than the divisor? The second fraction's denominator is a quadratic, so its numerator should be linear?
     
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  3. Jun 26, 2009 #2

    statdad

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    "Does it have to do with the fact that during synthetic division, the remainder is always 1 degree less than the divisor? The second fraction's denominator is a quadratic, so its numerator should be linear?"

    Essentially - the numerator should always be the "most general" polynomial of lower degree than the denominator
     
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