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 ...

The basic facts about separable extensions of discrete fields and factoring polynomials are developed in the constructive spirit of Errett Bishop. The ability to factor polynomials is shown to be ...

The previous method works perfectly well but only finds the remainder. To find the quotient as well, use synthetic division as follows. Now you need to factorise the second bracket. There's no point ...

We show that the binary expansions of algebraic numbers do not form secure pseudorandom sequences; given sufficiently many initial bits of an algebraic number, its minimal polynomial can be ...

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 ...