The graph of the rational function $\frac{2x^6+3x^5 - x^2 - 1}{q(x)}$  has a horizontal asymptote. What is the smallest possible degree of $q(x)$?
To find the horizontal asymptote of a rational function, I need to compare the degrees of the numerator and denominator. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. If the degree of the numerator is equal to the degree of the denominator, the horizontal asymptote is the ratio of the leading coefficients. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the x-axis (y=0). In this problem, the degree of the numerator is 6, so I need the degree of the denominator to be at least 6 as well. The smallest possible degree of $q(x)$ is 6, and that would make the horizontal asymptote $y=\frac{2}{a}$, where a is the leading coefficient of $q(x)$. 