Find a Polynomial Function F(x) of Least Possible Degree Having $f ( x ) = 2 ( x - 2 ) ^ { 2 } ( x + 1 )$

question 414

Multiple Choice

Find a polynomial function f(x) of least possible degree having the graph shown.
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• A) \(f ( x ) = 2 ( x - 2 ) ^ { 2 } ( x + 1 )\)
• B) \(f ( x ) = - 2 ( x - 2 ) ^ { 2 } ( x + 1 )\)
• C) \(f ( x ) = 2 ( x + 2 ) ^ { 2 } ( x - 1 )\)
• D) \(f ( x ) = - 2 ( x + 2 ) ^ { 2 } ( x - 1 )\)

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Definitions:

Bromine Substituent

Refers to a bromine atom attached to the carbon skeleton of an organic molecule, affecting its reactivity and properties.

Deactivator

A chemical compound or group that decreases the reactivity of an atom or a formation within a molecule, often used in reference to aromatic substitution reactions.

O,p-director

A term describing substituents on an aromatic ring that direct incoming substituents to the ortho and para positions in electrophilic aromatic substitution reactions.

Strongest Activating Group

A substituent that increases the reactivity of an aromatic ring toward electrophilic aromatic substitution reactions the most.