What is a polynomial?

A polynomial is fundamentally an algebraic expression that includes variables, coefficients, and employs the operations of addition, subtraction, and multiplication. It is essential that the exponents on the variables are non-negative integers. This means that in a polynomial, you can have terms such as 2x², 3x, or even a constant like 5, but you cannot have terms where the variable has a negative exponent or where the variable is located in the denominator, such as 1/x or x^(-1).

The definition in the answer option effectively captures all of these key characteristics. It emphasizes that the operations allowed extend beyond mere addition and subtraction — multiplication is also included. Since polynomials can be thought of in terms of their structure and the allowed operations, this broad definition encompasses the entire range of polynomials, from linear polynomials (like x + 2) to quadratic polynomials (like 2x² + 3x + 1) and beyond.

In contrast, other definitions are either too restrictive or omit crucial elements that need to be part of the description of a polynomial. For instance, just focusing on addition and subtraction or mentioning a linear equation with only two variables does not provide the complete picture of what constitutes