Jaime was asked to construct a polynomial function with the following zeros and multiplicities. Which function should he write?
Zero Multiplicity
x=4 1
x=−2 3
(1 point)
f(x)=(x−4)(x+2)
f(x)=(x+4)(x−2)
f(x)=(x+4)(x−2)^3
f(x)=(x−4)(x+2)^3
Jaime should write the function f(x)=(x−4)(x+2)^3.
To construct a polynomial function with the given zeros and multiplicities, Jaime needs to identify the factors of the function.
For each zero, the multiplicity indicates the number of times that zero appears as a factor.
Given zeros and multiplicities:
- x=4 (multiplicity 1)
- x=-2 (multiplicity 3)
To construct the polynomial function, we start with each factor raised to the power of its corresponding multiplicity.
Therefore, the correct function Jaime should write is:
f(x) = (x-4)(x+2)^3
This is because we have x-4 with multiplicity 1 and (x+2) with multiplicity 3.
To construct a polynomial function with the given zeros and multiplicities, we need to consider the factors associated with each zero.
For x = 4 with a multiplicity of 1, the factor is (x - 4).
For x = -2 with a multiplicity of 3, the factor is (x + 2)^3.
To construct the function, we multiply these factors together:
f(x) = (x - 4)(x + 2)^3
Therefore, the correct function that Jaime should write is f(x) = (x - 4)(x + 2)^3.