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 point) zeros at most

Answer 1

The degree of the polynomial \( f(x) = (x - 1)^3 (x + 7) \) can be determined by examining the factors.

1. The factor \( (x - 1)^3 \) contributes a degree of 3.
2. The factor \( (x + 7) \) contributes a degree of 1.

To find the total degree of the polynomial, we add the degrees of the individual factors:

\[ \text{Degree} = 3 + 1 = 4 \]

The greatest number of zeros a polynomial can have is equal to its degree. Therefore, the polynomial \( f(x) \) can have at most 4 zeros.

Thus, the answer is that the greatest number of zeros it could have is 4.