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Math Help - Factoring

  1. #1
    Junior Member
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    Factoring

    I have to evaluate a limit, which I know how to do, but the problem I'm having is the factoring.

    (x^3+2x^2-9x-18)/(x^2-9)

    I know the denominator factors to (x+3)(x-3) but I can't do the numerator when there's 3 different levels of exponents for x.

    Thanks

    - Adrian
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  2. #2
    MHF Contributor red_dog's Avatar
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    x^3+2x^2-9x-18=x^3-3x^2+5x^2-15x+6x-18=
    =x^2(x-3)+5x(x-3)+6(x-3)=(x-3)(x^2+5x+6)
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  3. #3
    MHF Contributor
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    Quote Originally Posted by Adrian View Post
    I have to evaluate a limit, which I know how to do, but the problem I'm having is the factoring.

    (x^3+2x^2-9x-18)/(x^2-9)

    I know the denominator factors to (x+3)(x-3) but I can't do the numerator when there's 3 different levels of exponents for x.

    Thanks

    - Adrian
    The numerator,
    x^3 +2x^2 -9x -18

    By just looking, you could see that (x+2) is in there.

    = (x^3 +2x^2) -(9x +18)
    = (x^2)(x+2) -9(x+2)
    = (x+2)(x^2 -9)

    So, your whole rational expression,
    (x^3+2x^2-9x-18)/(x^2-9)
    simplifies to
    (x+2)
    only.
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