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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.
Taylor's theorem gives an approximation of a -times differentiable function by a polynomial of degree k. The multivariate version of Taylor's theorem states that if f is a real-valued function of several variables, then for any point a and any direction v, there exists a polynomial P such that
Synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division. It can be used for division by linear or non-linear monic polynomials, and has various forms and applications in algebra.
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.
Learn about the history, statement, proof and applications of the Chinese remainder theorem, a mathematical result that relates congruences modulo pairwise coprime integers. The article also covers the generalization of the theorem to rings and combinatorics.
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.
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.