Thread: 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?

Originally Posted by iqbalkhan9

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?

$\displaystyle \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)}
$

$\displaystyle f(x)=\frac{x^3+x^2-6x}{x^2+2x-8}$

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

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

After simplification:

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

Vertical asymptote at x = -4

Point of discontinuity (hole) at x = 2