Definition

Noun: 1. (Mathematics): The process or result of breaking down a mathematical expression (such as a number or a polynomial) into a product of simpler factors. These factors, when multiplied together, yield the original entity.

Usage

• General Use: The term is used almost exclusively in mathematical contexts to describe the decomposition of an entity into its constituent multiplicative components.
  • The teacher explained the factorisation of quadratic equations.
  • Prime factorisation is a fundamental concept in number theory.

Advanced Usage

• Polynomial Factorisation: The process of expressing a polynomial as a product of its factors, which may be other polynomials or constants.
  • The factorisation of x² - 4 results in (x - 2)(x + 2).
• Integer Factorisation (or Factorization): The decomposition of a composite number into a product of smaller integers, particularly prime numbers.
  • The security of some encryption systems relies on the difficulty of integer factorisation.

Variants and Related Words

• Factor (verb): To resolve or break down into factors.
  • We need to factor this polynomial.
• Factorization (noun): An alternative spelling, primarily used in American English.
• Factorable (adjective): Capable of being factored.
  • Not all polynomials are factorable using real numbers.

Synonyms

• Decomposition (in a mathematical context)
• Resolution into factors
• Factoring (often used as a gerund to describe the process)

Notes on Different Meanings

The word 'factorisation' is highly specialized. It does not have common non-mathematical meanings, idiomatic uses, or associated phrasal verbs. Its usage is confined to technical discussions in mathematics and related fields like cryptography.

Noun

1. (mathematics) the resolution of an entity into factors such that when multiplied together they give the original entity