TITLE: Degree of a polynomial
QUESTION [6 upvotes]: If I have a polynomial, for example, $$ x^8 + x^2 + \dfrac{1}{x} $$ would this be considered to be of degree 8? I am working on a question involving the function $ \frac{1}{x} $ and I am wondering how this term affects the degree of the entire polynomial, if at all.

REPLY [3 votes]: The notion of degree is well-defined for rational functions. In this case, it is a rational function of degree $9$. The degree of a rational function $P(x)/Q(x)$ is $\max(\deg P,\deg Q)$ (where $P$ and $Q$ are polynomials with no common (nontrivial) factor and Q not identically zero).
You can see this because your function can be written as
$$f(x)=\frac{x^9 + x^3 + 1}{x}$$