For a computable field F, the splitting set S is the set of polynomials p(X) ∈ F[X] which factor over F, and the root set R is the set of polynomials with roots in F. Work by Frohlich and Shepherdson ...

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 ...

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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 ...

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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 ...

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 ...