Question
Based on the degree of the polynomial f(x)=(x−1)3(x+7)
, what is the greatest number of zeros it could have?(1 poin
, what is the greatest number of zeros it could have?(1 poin
Answers
GPT-4o mini
To determine the degree of the polynomial \( f(x) = (x - 1)^3 (x + 7) \), we need to look at the degree of each factor.
1. The factor \( (x - 1)^3 \) has a degree of 3.
2. The factor \( (x + 7) \) has a degree of 1.
To find the degree of the entire polynomial \( f(x) \), we add the degrees of the individual factors:
\[
\text{Degree of } f(x) = 3 + 1 = 4
\]
A polynomial of degree \( n \) can have at most \( n \) zeros (counting multiplicities). Since the degree of \( f(x) \) is 4, the greatest number of zeros it could have is 4.
Thus, the greatest number of zeros \( f(x) \) could have is:
\[
\boxed{4}
\]
1. The factor \( (x - 1)^3 \) has a degree of 3.
2. The factor \( (x + 7) \) has a degree of 1.
To find the degree of the entire polynomial \( f(x) \), we add the degrees of the individual factors:
\[
\text{Degree of } f(x) = 3 + 1 = 4
\]
A polynomial of degree \( n \) can have at most \( n \) zeros (counting multiplicities). Since the degree of \( f(x) \) is 4, the greatest number of zeros it could have is 4.
Thus, the greatest number of zeros \( f(x) \) could have is:
\[
\boxed{4}
\]