The verical asymptotes occuer at the zero's of the denominator

so we get

It does not have any horizontal asymptotes because the degree of the numerator is larger than the denominator.

It does have a slant asymptote( the degree of the numerator is one larger than the denominator) This can be calculated by dividing the denominator into the numerator. (long division)

Or by this trick

So the slant asymptotes is