Question 984101
When you do long division of the denominator into the numerator, you get (-x+3) in the quotient with remainder of -12x +31

If you multiply the denominator, unfactored, by (-x+3) and then add -12x +31, you will get the original function back.

The slant asymptote is -x+3
There are vertical asymptotes at x=-4 and x+3.

Note, in order to show the minus 1x slope, you need larger numbers on the calculator for x, like at least 50 or preferably 100.

{{{graph(300,300,-10,100,-50,100,(-x^3+2x^2+2x-5)/(x^2+x-12))}}}