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 ...

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 ...

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 ...

SIAM Journal on Numerical Analysis, Vol. 11, No. 6 (Dec., 1974), pp. 1087-1104 (18 pages) A composite algorithm has been designed for finding zeros of real polynomials. The algorithm has proved to 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 ...