Before being mortally wounded in a duel at age 20, Évariste Galois discovered the hidden structure of polynomial equations. By studying the relationships between their solutions — rather than the ...

We develop the concept of partition categories, in order to extend the Mullin-Rota theory of binomial enumeration, and simultaneously to provide a natural setting for recent applications of the ...

If \((x \pm h)\) is a factor of a polynomial, then the remainder will be zero. Conversely, if the remainder is zero, then \((x \pm h)\) is a factor. Often ...

Vesselin Dimitrov’s proof of the Schinzel-Zassenhaus conjecture quantifies the way special values of polynomials push each other apart. In the physical world, objects often push each other apart in an ...

This is a preview. Log in through your library . Abstract In this paper, Bernstein polynomials method (BPM) and their operational matrices are adopted to obtain approximate analytical solutions of ...

Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or ...

Two mathematicians have used a new geometric approach in order to address a very old problem in algebra. In school, we often learn how to multiply out and factor polynomial equations like (x² – 1) or ...

Here's how the process of synthetic division works, step-by-step. Divide \(3{x^3} - 4x + 5\) by \((x + 2)\) and state the quotient and remainder. First, make sure the polynomial is listed in order of ...