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 point)
Responses
f(x)=(x−1)3(x−81)5
f left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesis cubed left parenthesis x minus 81 right parenthesis superscript 5 baseline
f(x)=(x+1)5(x+81)3
f left parenthesis x right parenthesis equals left parenthesis x plus 1 right parenthesis superscript 5 baseline left parenthesis x plus 81 right parenthesis cubed
f(x)=(x−1)5(x−81)3
f left parenthesis x right parenthesis equals left parenthesis x minus 1 right parenthesis superscript 5 baseline left parenthesis x minus 81 right parenthesis cubed
f(x)=(x+1)3(x+81)5
f(x)=(x−1)5(x−81)3
To construct a polynomial function with the given zeros and multiplicities, Tatiana should write:
f(x) = (x - 1)^3 * (x - 81)^5
This means that the function should have a zero at x = 1 with a multiplicity of 3, and a zero at x = 81 with a multiplicity of 5.
To construct a polynomial function with the given zeros and multiplicities, we need to use the factored form of the function, where the zeros are expressed as factors.
The given zeros are x = 1 with a multiplicity of 3, and x = 81 with a multiplicity of 5.
The function should be written as f(x) = (x - 1)^3 * (x - 81)^5, which means that x = 1 is a zero with a multiplicity of 3, and x = 81 is a zero with a multiplicity of 5.
Therefore, the correct function that Tatiana should write is:
f(x) = (x - 1)^3 * (x - 81)^5.