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 ...

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First, we need to find which number when substituted into the equation will give the answer zero. \(f(1) = {(1)^3} + 4{(1)^2} + (1) - 6 = 0\) Therefore \((x - 1)\)is a factor. Factorise the quadratic ...

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 ...

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 Let 0 < θ < 1 be an irrational number with continued fraction expansion $\theta =[a_{1},a_{2},a_{3},\ldots ...