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  2. Factorization - Wikipedia

    en.wikipedia.org/wiki/Factorization

    In mathematics, factorization (or factorisation, see English spelling differences) or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller or simpler objects of the same kind. For example, 3 × 5 is an integer factorization of 15, and (x – 2) (x + 2) is a polynomial ...

  3. Factorization of polynomials - Wikipedia

    en.wikipedia.org/wiki/Factorization_of_polynomials

    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 ...

  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: That difference is algebraically factorable as ; if neither factor equals one, it is a proper factorization of N. Each odd number has such a representation. Indeed, if is a factorization of N, then.

  5. Completing the square - Wikipedia

    en.wikipedia.org/wiki/Completing_the_square

    Animation depicting the process of completing the square. (Details, animated GIF version) In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form ⁠ ⁠ to the form ⁠ ⁠ for some values of ⁠ ⁠ and ⁠ ⁠. [1] In terms of a new quantity ⁠ ⁠, this expression is a quadratic ...

  6. Euler method - Wikipedia

    en.wikipedia.org/wiki/Euler_method

    In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.

  7. Integer factorization - Wikipedia

    en.wikipedia.org/wiki/Integer_factorization

    For example, if n = 171 × p × q where p < q are very large primes, trial division will quickly produce the factors 3 and 19 but will take p divisions to find the next factor. As a contrasting example, if n is the product of the primes 13729, 1372933, and 18848997161, where 13729 × 1372933 = 18848997157, Fermat's factorization method will ...