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Learn the definition, proof and applications of the polynomial remainder theorem, which states that a polynomial is the sum of a polynomial and the product by a polynomial of lower degree. See examples, formulas and references for this algebraic concept.
Ruffini's rule is a method for dividing a polynomial by a binomial of the form x – r. It can be used for polynomial factorization and was invented by Paolo Ruffini in 1809.
A polynomial is a mathematical expression involving addition, subtraction, multiplication and exponentiation of variables and coefficients. Learn how to write, classify and manipulate polynomials, and see examples and applications in various fields of mathematics and science.
A remainder is the amount "left over" after dividing one number by another, or after subtracting one number from another. Learn how to calculate remainders for integers, floating-point numbers, and polynomials, and see different conventions in programming languages.
Bézout's theorem is a statement in algebraic geometry concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that in general the number of common zeros equals the product of the degrees of the polynomials. [1] It is named after Étienne Bézout.
The factor theorem connects polynomial factors with polynomial roots. It states that a polynomial is a factor of another polynomial if and only if it is a root of the latter. See proofs, examples and applications of the theorem.
Download as PDF; Printable version; ... , expressed by the Chinese remainder theorem as ... are all even (in our running example, they are 8, 6, 2, 10, 4.)
Download as PDF; Printable version; ... a product of separable polynomials. The simplest such example is the following. ... remainder theorem applied to the ...