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

1 answer

To construct a polynomial function with the given zeros and multiplicities, we can use the factored form of a polynomial.

Since x = 1 has a multiplicity of 3, it means that (x - 1) is a factor of the polynomial function.

Similarly, since x = 81 has a multiplicity of 5, it means that (x - 81) is also a factor of the polynomial function.

To find the polynomial function, we can multiply these factors together:

f(x) = (x - 1)^3 * (x - 81)^5