What does it mean for a polynomial to be degree n?

A polynomial is defined as an expression that consists of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication with coefficients. The degree of a polynomial is determined by the highest exponent of the variable in the polynomial.

When we say a polynomial is of degree ( n ), we specifically mean that among all the terms in the polynomial, the term with the highest exponent has ( n ) as its exponent. For instance, in the polynomial ( 4x^3 + 2x^2 - x + 7 ), the highest exponent on the variable ( x ) is 3, indicating that this polynomial is of degree 3.

This concept is critical because the degree of the polynomial helps to define its behavior, such as the shape of its graph and the number of roots it may have. Higher-degree polynomials may exhibit more complex behaviors compared to lower-degree ones.

The other choices do not accurately reflect the definition of a polynomial's degree. The number of terms in the polynomial, the coefficient of the term, or describing a polynomial as a constant do not pertain to the degree, which is strictly about the highest exponent. Therefore, the correct understanding is that a polynomial is of degree ( n \