Which of the following properly describes the relationship between the degree of a polynomial and the number of zeros it has?(1 point)
Responses
The degree of the polynomial is the least number of zeros the polynomial could have.
The degree of the polynomial is the least 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 greatest number of zeros the polynomial could have.
The degree of the polynomial is the greatest number of zeros the polynomial could have.
The correct response is:
The degree of the polynomial is the greatest number of zeros the polynomial could have.
The correct description of the relationship between the degree of a polynomial and the number of zeros it has is: "The degree of the polynomial is the greatest number of zeros the polynomial could have."
To understand this relationship, it is important to have a basic understanding of polynomials. A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
The degree of a polynomial is determined by the highest power of the variable in the expression. For example, in the polynomial "3x^2 + 2x - 1", the highest power of x is 2, so the degree of the polynomial is 2.
Zeros of a polynomial, also known as roots, are the values of the variable that make the polynomial equal to zero. In other words, they are the solutions to the equation formed by setting the polynomial equal to zero.
The Fundamental Theorem of Algebra states that a polynomial of degree n will have exactly n zeros, counting both real and complex zeros. However, it is important to note that a polynomial can have fewer real zeros than its degree, but it cannot have more.
Therefore, the degree of a polynomial serves as an upper bound on the number of zeros it can have. For example, a polynomial of degree 3 can have at most 3 zeros, while a polynomial of degree 4 can have at most 4 zeros.
In summary, the degree of a polynomial is the greatest number of zeros the polynomial could have.