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  2. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    Factorization is one of the most important methods for expression manipulation for several reasons. If one can put an equation in a factored form E⋅F = 0, then the problem of solving the equation splits into two independent (and generally easier) problems E = 0 and F = 0. When an expression can be factored, the factors are often much simpler ...

  3. Factorization of polynomials - Wikipedia

    en.wikipedia.org/wiki/Factorization_of_polynomials

    In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain. Polynomial factorization is one of the fundamental components of computer algebra systems.

  4. Fermat's factorization method - Wikipedia

    en.wikipedia.org/wiki/Fermat's_factorization_method

    Fermat's factorization method, named after Pierre de Fermat, is based on the representation of an odd integer as the difference of two squares: N = a 2 − b 2 . {\displaystyle N=a^{2}-b^{2}.} That difference is algebraically factorable as ( a + b ) ( a − b ) {\displaystyle (a+b)(a-b)} ; if neither factor equals one, it is a proper ...

  5. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    In mathematics, a polynomial is a ... called factorization is, in general, ... A matrix polynomial equation is an equality between two matrix polynomials, ...

  6. FOIL method - Wikipedia

    en.wikipedia.org/wiki/FOIL_method

    The FOIL method is a special case of a more general method for multiplying algebraic expressions using the distributive law.The word FOIL was originally intended solely as a mnemonic for high-school students learning algebra.

  7. QR decomposition - Wikipedia

    en.wikipedia.org/wiki/QR_decomposition

    If A is invertible, then the factorization is unique if we require the diagonal elements of R to be positive. If instead A is a complex square matrix, then there is a decomposition A = QR where Q is a unitary matrix (so the conjugate transpose Q † = Q − 1 {\displaystyle Q^{\dagger }=Q^{-1}} ).

  8. Matrix decomposition - Wikipedia

    en.wikipedia.org/wiki/Matrix_decomposition

    In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems.

  9. Fundamental theorem of arithmetic - Wikipedia

    en.wikipedia.org/wiki/Fundamental_theorem_of...

    In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors. [3] [4] [5] For example,