How many vertical asymptotes can a rational function have?

Suppose ${\displaystyle f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}}$ where ${\displaystyle p\left(x\right)}$ and ${\displaystyle q\left(x\right)}$ are polynomials.
If ${\displaystyle q\left(x_1\right)=0}$ and ${\displaystyle p\left(x_1\right)\ne 0}$ then ${\displaystyle f\left(x\right)}$ will have a vertical asymptote at ${\displaystyle x=x_1}$.
If ${\displaystyle q\left(x_1\right)=0}$ and ${\displaystyle p\left(x_1\right)=0}$ then ${\displaystyle f\left(x\right)}$ will have a vertical asymptote at ${\displaystyle x=x_1}$ if and only if the multiplicity of this zero of ${\displaystyle q\left(x\right)}$ is greater than the multiplicity of this zero of ${\displaystyle p\left(x\right)}$.
Therefore, the number of zeros is the largest number of vertical asymptotes that can exist of ${\displaystyle q\left(x\right)}$, which is at most the degree of ${\displaystyle q\left(x\right)}$.