Question

what is the difference between a polynomial expression and a polynomial function?

Answer 1

A polynomial expression in one or more given entities E1, E2, ..., is any meaningful expression constructed from copies of those entities together with constants, using the operations of addition and multiplication.

A polynomial function is a function that can be defined by evaluating a polynomial.

Answer 2

Example:
\[\text{expression:}~~x^2+4x+4\\
\text{function:}~~f(x)=x^2+4x+4\\
~~~~~~~~~~~~(output)=(input)^2+4(input)+4\]