Question

How do you tell if something is a polynomial?

Answer 1

Something is polynomial if it's just a bunch of positive powers of x added up/multiplied together. It'll usually look something like:
\[ax^3+bx^2+cx+d\]

If you start dividing by x, using logs, trig functions, raising things to the x power then it stops being polynomial and becomes rational, logarithmic, trigonometric, exponential, etc.

Keep in mind that sometimes you can simplify something that looks weird to become a polynomial too.