Greg was asked to construct a polynomial function with the following zeros and multiplicities. Which function should he write?
Zero Multiplicity
x=−4 2
x=2 3
Function #1: f(x)=(x+4)(x−2)
Function #2: f(x)=(x+4)2(x−2)^3
Function #3: f(x)=(x−4)2(x+2)^3
Function #2: f(x)=(x+4)2(x−2)^3
To construct a polynomial function with given zeros and multiplicities, we need to use the factored form of a polynomial. The multiplicities indicate how many times a zero appears in the factored form.
Looking at the given zeros and multiplicities:
Zero: x = -4
Multiplicity: 2
Zero: x = 2
Multiplicity: 3
Using this information, we can write the function:
Function #2: f(x) = (x + 4)^2 * (x - 2)^3
Therefore, Greg should write Function #2.