Which of the following properly describes the relationship between the degree of a polynomial and the number of zeros it has?(1 point)

Question

Responses

The degree of the polynomial is the greatest number of zeros the polynomial could have.
The degree of the polynomial is the greatest number of zeros the polynomial could have.

The degree of the polynomial is half the number of zeros.
The degree of the polynomial is half the number of zeros.

The degree of the polynomial is double the number of zeros.
The degree of the polynomial is double the number of zeros.

The degree of the polynomial is the least number of zeros the polynomial could have.

Answer 1

The correct response is:

The degree of the polynomial is the greatest number of zeros the polynomial could have.

In general, a polynomial of degree \( n \) can have up to \( n \) real roots (or zeros), counting multiplicities. Thus, the degree indicates the maximum potential number of zeros, but not all zeros must be real (some may be complex), and not all zeros may be distinct.