I have looked it up on google, though I don't quite understand it (yes long division if the leading coefficient ended up being higher or something)... I don't quite understand so I might need some examples for 3U and 4U perhaps

Situations beyond polynomial long division will never occur in 3U. You should provide your own examples (along with any questions that you have regarding it).

Also note that if the degree of the polynomial in the numerator is

**not** exactly 1 higher than the degree of the denominator, then there will

**not** be an oblique asymptote. In general, if the degree of the polynomial is the numerator is less, we can only ever have horizontal asymptotes.

The occurrence of these in 4U are really handled case-by-case. These examples are hard to single out because you never know whether or not they will be examined (i.e. they are rare). Most of the time, if they appear in 4U then they require the same methods in 3U, however they could occasionally occur from something more mysterious (e.g. sketching \( y = x\, f(x) \) given that \(y = f(x) \) has a horizontal asymptote that's not at \(y=0\)).