Try either synthetic division or polynomial division.
Root of the denominator is 2.
2 | 1 3 -2
| 2 10
|_____________________
1 5 8
f(x) can be expressed as .
This means, as x goes increasingly toward negative or positive infinity, f approaches the line , because the remainder becomes increasingly small.
Know clearly, this is NOT a horizontal asymptote; it is a slant asymptote.