for an irreducible, rational polynomial function, if the degree of the numerator is one greater than the degree of the denominator, then the graph of the rational function will have a slant asymptote.

for example ...

... note the polynomial is irreducible and the degree of the numerator is one greater than the degree of the denominator.

perform the long division.

you should get the quotient with a remainder.

the slant asymptote is