What defines a polynomial?

A polynomial is defined as an expression made up of variables and coefficients, where these variables are raised to non-negative integer powers and combined through the operations of addition, subtraction, and multiplication. This means that for an expression to be classified as a polynomial, it can consist of multiple terms that adhere to these rules, such as (3x^2 + 2x - 5), which includes coefficients (numbers multiplied by variables) and variables raised to whole number powers.

The other choices describe different mathematical concepts that do not fit the specific criteria of a polynomial. A constant value or number alone does not constitute a polynomial unless it is considered a special case of a polynomial of degree zero. An equation illustrating a relationship between variables might represent many forms of expressions, including non-polynomials, while a function that only includes variables without any constants or specified operations does not align with the definition of a polynomial either. Therefore, the first choice is the only one that correctly encapsulates the definition of a polynomial.