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- Factorization abstract "In mathematics, factorization (also factorisation in some forms of British English) or factoring is the decomposition of an object (for example, a number, a polynomial, or a matrix) into a product of other objects, or factors, which when multiplied together give the original. For example, the number 15 factors into primes as 3 × 5, and the polynomial x2 − 4 factors as (x − 2)(x + 2). In all cases, a product of simpler objects is obtained.The aim of factoring is usually to reduce something to “basic building blocks”, such as numbers to prime numbers, or polynomials to irreducible polynomials. Factoring integers is covered by the fundamental theorem of arithmetic and factoring polynomials by the fundamental theorem of algebra. Viète's formulas relate the coefficients of a polynomial to its roots.The opposite of polynomial factorization is expansion, the multiplying together of polynomial factors to an “expanded” polynomial, written as just a sum of terms.Integer factorization for large integers appears to be a difficult problem. There is no known method to carry it out quickly. Its complexity is the basis of the assumed security of some public key cryptography algorithms, such as RSA.A matrix can also be factorized into a product of matrices of special types, for an application in which that form is convenient. One major example of this uses an orthogonal or unitary matrix, and a triangular matrix. There are different types: QR decomposition, LQ, QL, RQ, RZ.Another example is the factorization of a function as the composition of other functions having certain properties; for example, every function can be viewed as the composition of a surjective function with an injective function. This situation is generalized by factorization systems.".
- Factorization thumbnail Factorisatie.svg?width=300.
- Factorization wikiPageExternalLink factors.evalwave.com.
- Factorization wikiPageExternalLink factor.en.
- Factorization wikiPageExternalLink v=onepage&q&f=false.
- Factorization wikiPageID "82341".
- Factorization wikiPageLength "26918".
- Factorization wikiPageOutDegree "86".
- Factorization wikiPageRevisionID "681779055".
- Factorization wikiPageWikiLink Abel-Ruffini_theorem.
- Factorization wikiPageWikiLink Abel–Ruffini_theorem.
- Factorization wikiPageWikiLink Algebraic_expression.
- Factorization wikiPageWikiLink Algebraic_formula.
- Factorization wikiPageWikiLink Algebraic_number.
- Factorization wikiPageWikiLink Algorithm.
- Factorization wikiPageWikiLink American_and_British_English_spelling_differences.
- Factorization wikiPageWikiLink Binomial_theorem.
- Factorization wikiPageWikiLink Category:Arithmetic.
- Factorization wikiPageWikiLink Category:Elementary_algebra.
- Factorization wikiPageWikiLink Characteristic_(algebra).
- Factorization wikiPageWikiLink Completing_the_square.
- Factorization wikiPageWikiLink Complex_conjugate.
- Factorization wikiPageWikiLink Complex_conjugate_root_theorem.
- Factorization wikiPageWikiLink Complex_number.
- Factorization wikiPageWikiLink Computer_algebra_system.
- Factorization wikiPageWikiLink Coprime_integers.
- Factorization wikiPageWikiLink Cubic_equation.
- Factorization wikiPageWikiLink Cubic_function.
- Factorization wikiPageWikiLink Difference_of_two_squares.
- Factorization wikiPageWikiLink Distributive_property.
- Factorization wikiPageWikiLink Divisor.
- Factorization wikiPageWikiLink Eulers_factorization_method.
- Factorization wikiPageWikiLink FOIL_method.
- Factorization wikiPageWikiLink Factor_theorem.
- Factorization wikiPageWikiLink Factorization_of_polynomials.
- Factorization wikiPageWikiLink Factorization_system.
- Factorization wikiPageWikiLink Fermats_factorization_method.
- Factorization wikiPageWikiLink Field_(mathematics).
- Factorization wikiPageWikiLink Function_(mathematics).
- Factorization wikiPageWikiLink Function_composition.
- Factorization wikiPageWikiLink Fundamental_theorem_of_algebra.
- Factorization wikiPageWikiLink Fundamental_theorem_of_arithmetic.
- Factorization wikiPageWikiLink Injective_function.
- Factorization wikiPageWikiLink Integer.
- Factorization wikiPageWikiLink Integer_factorization.
- Factorization wikiPageWikiLink Irreducible_polynomial.
- Factorization wikiPageWikiLink Mathematics.
- Factorization wikiPageWikiLink Matrix_(math).
- Factorization wikiPageWikiLink Matrix_(mathematics).
- Factorization wikiPageWikiLink Monoid_factorisation.
- Factorization wikiPageWikiLink Multiplication.
- Factorization wikiPageWikiLink Multiplicative_partition.
- Factorization wikiPageWikiLink Nth_root.
- Factorization wikiPageWikiLink Number.
- Factorization wikiPageWikiLink Orthogonal_matrix.
- Factorization wikiPageWikiLink Partition_(number_theory).
- Factorization wikiPageWikiLink Pascals_triangle.
- Factorization wikiPageWikiLink Polynomial.
- Factorization wikiPageWikiLink Polynomial_expansion.
- Factorization wikiPageWikiLink Polynomial_factorization.
- Factorization wikiPageWikiLink Polynomial_greatest_common_divisor.
- Factorization wikiPageWikiLink Polynomial_long_division.
- Factorization wikiPageWikiLink Prime_factor.
- Factorization wikiPageWikiLink Prime_factorization.
- Factorization wikiPageWikiLink Prime_number.
- Factorization wikiPageWikiLink Product_(mathematics).
- Factorization wikiPageWikiLink Program_synthesis.
- Factorization wikiPageWikiLink Public-key_cryptography.
- Factorization wikiPageWikiLink Public_key_cryptography.
- Factorization wikiPageWikiLink QR_decomposition.
- Factorization wikiPageWikiLink Quadratic_formula.
- Factorization wikiPageWikiLink Quadratic_function.
- Factorization wikiPageWikiLink Quadratic_polynomial.
- Factorization wikiPageWikiLink Quartic_equation.
- Factorization wikiPageWikiLink Quartic_function.
- Factorization wikiPageWikiLink RSA_(algorithm).
- Factorization wikiPageWikiLink RSA_(cryptosystem).
- Factorization wikiPageWikiLink Radical_expression.
- Factorization wikiPageWikiLink Rational_root_test.
- Factorization wikiPageWikiLink Rational_root_theorem.
- Factorization wikiPageWikiLink Real_number.
- Factorization wikiPageWikiLink Relatively_prime.
- Factorization wikiPageWikiLink Robert_Recorde.
- Factorization wikiPageWikiLink Root_of_a_function.
- Factorization wikiPageWikiLink Surjective_function.
- Factorization wikiPageWikiLink Synthetic_division.
- Factorization wikiPageWikiLink Table_of_Gaussian_integer_factorizations.
- Factorization wikiPageWikiLink Thomas_Harriot.
- Factorization wikiPageWikiLink Triangular_matrix.
- Factorization wikiPageWikiLink Unitary_matrix.
- Factorization wikiPageWikiLink Univariate.
- Factorization wikiPageWikiLink Vietas_formulas.
- Factorization wikiPageWikiLink Vixc3xa8tes_formulas.
- Factorization wikiPageWikiLink Wolfram_Alpha.
- Factorization wikiPageWikiLink Zero_of_a_function.
- Factorization wikiPageWikiLink File:A_plus_b_au_carre.svg.
- Factorization wikiPageWikiLink File:Differenceofcubes.jpg.
- Factorization wikiPageWikiLink File:Factorisatie.svg.
- Factorization wikiPageWikiLinkText "Factor".
- Factorization wikiPageWikiLinkText "Factored order".