Note that if you want to figure out if a function has a slant asymptote, you have to realize that the equation of a slant asymptote is linear, so the exponent of the leading coefficient of the numerator of the function must be one greater than that of the denominator.

When doing long division (denominator into numerator), it might not divide evenly. Do not concern yourself with the remainder. That slant or oblique asymptote is just the linear portion.