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Math Help - How to factor this rational function and characteristics? (x^3+x^2-6x)/(x^2+2x-8)

  1. #1
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    How to factor this rational function and characteristics? (x^3+x^2-6x)/(x^2+2x-8)

    How to factor this rational function and characteristics?
    (x^3+x^2-6x)/(x^2+2x-8)

    I can't factor the numerator to find the x intercepts and some other things, which i have to do ALGEBRAICALLY. Also this is what i have so far for the characteristics.

    Domain - (-infinity, + infinity) ?
    Range - (-infinity, -4) U (-4,2) U (2, +infinity)
    Local Max (-6.-9) Local min (-2,-1) no absolute max/mins?
    Increasing Intervals (-infinity, -9) (-1, +infinity)
    Decreasing Intervals (-9, +infinity) (+infinity, -1)
    Y intercept (0,0) and X Intercept (-3,0) < i used my calculator :\
    Holes & discontinuities ?
    function is odd
    rate of change?
    end behavior?
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  2. #2
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    Quote Originally Posted by iqbalkhan9 View Post
    How to factor this rational function and characteristics?
    (x^3+x^2-6x)/(x^2+2x-8)

    I can't factor the numerator to find the x intercepts and some other things, which i have to do ALGEBRAICALLY. Also this is what i have so far for the characteristics.

    Domain - (-infinity, + infinity) ?
    Range - (-infinity, -4) U (-4,2) U (2, +infinity)
    Local Max (-6.-9) Local min (-2,-1) no absolute max/mins?
    Increasing Intervals (-infinity, -9) (-1, +infinity)
    Decreasing Intervals (-9, +infinity) (+infinity, -1)
    Y intercept (0,0) and X Intercept (-3,0) < i used my calculator :\
    Holes & discontinuities ?
    function is odd
    rate of change?
    end behavior?
    \frac{x^3+x^2-6x}{x^2+2x-8} = \frac{x(x^2+x-6)}{(x+4)(x-2)} = \frac{x(x+3)(x-2)}{(x+4)(x-2)}<br />
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  3. #3
    A riddle wrapped in an enigma
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    f(x)=\frac{x^3+x^2-6x}{x^2+2x-8}

    f(x)=\frac{x(x+3)(x-2)}{(x+4)(x-2)}

    Restrictions on the domain: x \ne -4 and x \ne 2

    After simplification:

    f(x)=\frac{x(x+3)}{x+4}

    Vertical asymptote at x = -4

    Point of discontinuity (hole) at x = 2
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