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
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
To construct a polynomial function with the given zeros and multiplicities, we need to write the function in factored form.
Since the zero x = 1 has a multiplicity of 3, it means that (x - 1) appears as a factor three times in the factored form of the polynomial function.
Similarly, since the zero x = 81 has a multiplicity of 5, it means that (x - 81) appears as a factor five times in the factored form of the polynomial function.
Therefore, the function that Tatiana should write is:
f(x) = (x - 1)^3 * (x - 81)^5
To construct a polynomial function with the given zeros and multiplicities, we can use the fact that if a number "a" is a zero of a polynomial function with multiplicity "m", then the function can be written as a product of factors, where each factor is raised to the power of its corresponding multiplicity.
In this case, we have two zeros: x = 1 with multiplicity 3, and x = 81 with multiplicity 5. So, the polynomial function can be written as:
(x - 1)^3 * (x - 81)^5
Expanding this expression gives us the polynomial function Tatiana should write.