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 ...

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 ...

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 ...

Synthetic division is another, easier, way of carrying out division of polynomials. Look at how it would work for the example above before moving on to an explanation of the process.