Question 1157351
<br>
There is no oblique asymptote.<br>
The numerator is degree 3, the denominator is degree 1.  The quotient is degree 2, so the asymptote is a parabola, not a line.  By the formal definition, an oblique asymptote is a line.<br>
Perform the indicated division, either with long division or synthetic division.  The result will be<br>
{{{(x^3+4x+1)/(x-2) = x^2+2x+8+9/(x-2)}}}<br>
The asymptote will be the quadratic function x^2+2x+8.<br>
Here is graph of the function and its asymptote.<br>
{{{graph(400,400,-10,10,-10,80,(x^3+4x+1)/(x-2),x^2+2x+8)}}}<br>