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)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)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)

Answer 1

To construct a polynomial function based on the given zeros and multiplicities, we start with the zeros and their associated multiplicities:

1. Zero at \( x = 4 \) with multiplicity 1 means we include the factor \( (x - 4) \).
2. Zero at \( x = -2 \) with multiplicity 3 means we include the factor \( (x + 2)^3 \).

Combining these factors, the polynomial function \( f(x) \) can be expressed as:

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

The correct response from the provided options is:

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