Question

aime 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)3
f left parenthesis x right parenthesis equals left parenthesis x minus 4 right parenthesis left parenthesis x plus 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)
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
Skip to navigation
page 14 of 14

Answer 1

To construct a polynomial function based on the given zeros and their respective multiplicities, we start by noting the zeros and how they contribute to the factors of the polynomial:

1. The zero \( x = 4 \) has a multiplicity of 1, which means the factor is \( (x - 4) \).
2. The zero \( x = -2 \) has a multiplicity of 3, which means the factor is \( (x + 2)^3 \).

Combining these factors, the polynomial function is:

\[
f(x) = (x - 4)(x + 2)^3
\]

Given the options, this matches the first response:

**f(x) = (x - 4)(x + 2)³**

So the correct function Aime should write is:

**f(x) = (x - 4)(x + 2)³**