Write the least-degree polynomial that crosses the \(x\text{-}\text{axis}\) at \(0\), flattens while crossing at \(2\), and has leading coefficient \(1\).

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f(x) = x(x − 2)³(x + 1)². It has an unrequested zero and is not least degree.

f(x) = x(x − 2)³. It crosses at both zeros, has flattening at 2, and has leading coefficient 1.

f(x) = x(x − 2)². The zero at 2 touches instead of flattening while crossing.

f(x) = −x(x − 2)³. It has the behavior, but its leading coefficient is −1.

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Curriculum context

Course: Math III
Standard: F-IF.7.c
Category: Functions
Domain: Interpreting Functions
Objective: Graph polynomial functions using zeros, factorizations, and end behavior.
Problem type: Build the least-degree polynomial from graph behaviors