Tatiana was asked to construct a polynomial function with the following zeros and multiplicities. Which function should she write?
Zero Multiplicity
x=1 3
x=81 5
f(x)=(x+1)^3(x+81)^5
f(x)=(x-1)^3(x-81)^5
f(x)=(x-1)^5(x-81)^3
f(x)=(x+1)^5(x+81)^3
f(x)=(x-1)^3(x-81)^5
To construct a polynomial function with the given zeros and multiplicities, Tatiana needs to use the factored form of a polynomial.
The function she should write is f(x) = (x+1)^3 * (x+81)^5, which corresponds to the first option: f(x) = (x+1)^3(x+81)^5.
This is because when a zero has a multiplicity of 3, it means it appears as a factor 3 times in the function. Similarly, when a zero has a multiplicity of 5, it means it appears as a factor 5 times in the function.