Find a Polynomial of Degree 3 That Has Zeros 1 $x ^ { 2 }$

question 143

Essay

Find a polynomial of degree 3 that has zeros 1, 2, and -5 and in which the coefficient of $x ^ { 2 }$ is 3.

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Definitions:

Regiochemistry

This term relates to the orientation of the addition or substitution of a chemical bond in a molecule, determining the structure of the resulting product.

Cycloaddition

A chemical reaction in which two or more unsaturated molecules (or parts of the same molecule) combine to form a cyclic compound.

Sigmatropic Rearrangement

A type of pericyclic reaction in which a σ-bond (sigma bond) changes position relative to a π system (pi system) within a molecule, following specific suprafacial or antarafacial pathways.

Diels-Alder

A chemical reaction between a diene and a dienophile, resulting in the formation of a cyclohexene derivative.