To determine the correct polynomial function based on the given zeros and their multiplicities, we need to look at the provided options while focusing on the numerical values of the zeros and their respective multiplicities.
The first option has the zeros at
The second option has the zeros at
The third option has the zeros at
The fourth option has the zeros at
To construct the right polynomial, we must take into account that the zeros must be listed with the correct values and corresponding multiplicities. If we denote the zeros as
Thus, the correct function that Tatiana should write is:
f(x) = (x−1)^5 (x−81)^3