We develop an understanding of the relationship between the symmetry of polynomial graphs and the calculus that underlies this symmetry. We arrive at a method to determine whether a single-variable polynomial with real coefficients has a symmetric graph. We then encode this method into a closed formula that is a necessary and sufficient condition for the polynomial to have symmetry.
Cermak, Peter A.
"A Single Criterion for Polynomial Symmetry,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 23:
1, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol23/iss1/5