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)
Responses
f(x)=(x−4)(x+2)
f left parenthesis x right parenthesis equals left parenthesis x minus 4 right parenthesis left parenthesis x plus 2 right parenthesis
f(x)=(x+4)(x−2)3
f left parenthesis x right parenthesis equals left parenthesis x plus 4 right parenthesis left parenthesis x minus 2 right parenthesis cubed
f(x)=(x+4)(x−2)
f left parenthesis x right parenthesis equals left parenthesis x plus 4 right parenthesis left parenthesis x minus 2 right parenthesis
f(x)=(x−4)(x+2)3
f left parenthesis x right parenthesis equals left parenthesis x minus 4 right parenthesis left parenthesis x plus 2 right parenthesis cubed
Jaime should write the polynomial function: 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 given zeros and multiplicities, you need to use the factors of the zeros with their corresponding multiplicities.
In this case, the given zeros are x = 4 and x = -2, with multiplicities 1 and 3 respectively.
To construct the polynomial function, multiply the factors corresponding to each zero by the multiplicity.
So, the correct answer would be:
f(x) = (x - 4)(x + 2)³
Therefore, the correct function Jaime should write is:
f(x) = (x - 4)(x + 2)³