Question

What is the relationship between the degree of a polynomial and the number of zeros and factors it has?(1 point) Responses There is no relationship. There is no relationship. According to the Fundamental Theorem of Algebra, the number of zeros and factors is equal to the polynomial's degree minus 1 According to the Fundamental Theorem of Algebra, the number of zeros and factors is equal to the polynomial's degree minus 1 According to the Fundamental Theorem of Algebra, the number of zeros and factors is equal to the polynomial's degree. According to the Fundamental Theorem of Algebra, the number of zeros and factors is equal to the polynomial's degree. The degree of the polynomial tells us how many x-intercepts there are but does not tell us how many solutions there are.

Answer 1

The correct response is: According to the Fundamental Theorem of Algebra, the number of zeros and factors is equal to the polynomial's degree.

This theorem states that a polynomial of degree \( n \) will have exactly \( n \) roots (counting multiplicities) in the complex number system. This implies that a polynomial can be factored into \( n \) linear factors (if you include complex factors) or \( n \) real roots depending on the nature of the roots.