Bot GPT 4-o mini 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:
- The zero \( x = 4 \) has a multiplicity of 1, which means the factor is \( (x - 4) \).
- 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
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