SOLUTION: for the function Q(x) sate the behavior of the function at each of the asymptotes. [Oblique Asymptote (x-5), Vertical Asymptote x=-2 & x=-1] Q(x) = (x^3-2x^2-5x+6)/(x^2+3x+2)

Question 1041997: for the function Q(x) sate the behavior of the function at each of the asymptotes. [Oblique Asymptote (x-5), Vertical Asymptote x=-2 & x=-1]
Q(x) = (x^3-2x^2-5x+6)/(x^2+3x+2)
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!

Vertical asymptotes x=-1 and x=-2, and possible sign change in Q(x) at each asymptote. Why vertical asymptotes? Undefined at those x values.

              x  -5
          ________________________
x^2+3x+2  |   x^3-2x^2-5x+6
          |
          |   x^3+3x^2+2x
          |_______________
              0 -5x^2-7x+6               Bring down the 6.
                -5x^2-10x-10
                --------------
                  0  3x+16

The non-remainder part of the quotient is , and the remainder part is ; this remainder will become increasingly small and approach 0 as x goes to the left or to the right unbounded. The oblique asymptote for Q is .

The exact behavior for the vertical asymptotes, I did not analyze for you.
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