Newton-like Identities from Synthetic Division
Michael A. Jones
Associate Editor
Mathematical Reviews
American Mathematical Society
I will recall and then prove Vieta's formulas that relate the roots of a polynomial to its coefficients. I will explain Euler's proof of Newton's identities that relate the coefficients of a polynomial to the sums of powers of its roots. Finally, I'll explain how to view synthetic division from a linear algebra point of view and use this approach to prove an identity in the spirit of Newton.