factoring

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factoring

A student writes a factoring problem on the chalkboard.

Definition

Noun: 1. (Mathematics) The process or operation of resolving a number or mathematical expression into its constituent factors (components that, when multiplied together, produce the original entity). 2. (Finance/Commerce) The business or financial practice of selling accounts receivable to a third party (a factor) at a discount to obtain immediate cash. Note: This meaning is a distinct, specialized usage of the word derived from the financial term 'factor,' not directly from the mathematical process.

Usage
  • The term factoring is used as a gerund (a verb form functioning as a noun) to describe the action or process of finding factors.
  • In mathematics, it is a fundamental technique in algebra and arithmetic.
  • In finance, it describes a specific transaction.
Examples
  • Mathematics:
    • The factoring of the polynomial x² - 5x + 6 results in (x - 2)(x - 3).
    • We will study the factoring of quadratic equations in this chapter.
    • Simplifying the expression requires factoring the numerator and denominator.
  • Finance:
    • The small company used invoice factoring to improve its cash flow.
    • Factoring provides businesses with immediate working capital.
Advanced Usage
  • Prime Factoring/Factorization: The process of breaking down a composite number into its prime factors (e.g., the prime factoring of 12 is 2 x 2 x 3).
  • Common Factoring: Factoring out a common factor shared by all terms in an expression (e.g., factoring from ).
Variants and Related Words
  • Factor (verb): To resolve into factors.
  • Factor (noun):
    • (Mathematics) A number or algebraic expression that divides another number or expression evenly.
    • (General) An element or circumstance that contributes to a result.
    • (Finance) A company that purchases accounts receivable.
  • Factorization/Factorisation (noun): Synonymous with the mathematical meaning of 'factoring,' often used interchangeably.
  • Refactoring (noun): A term in computer programming meaning restructuring existing code without changing its external behavior.
Synonyms
  • (Mathematics): Factorization, resolution into factors, decomposition.
  • (Finance): Invoice discounting, accounts receivable financing.
Related Phrases
  • Factoring out: The act of removing a common factor from an expression.
    • By factoring out a 3, the equation becomes simpler.
  • Factoring by grouping: A method used to factor polynomials with four or more terms.
factoring

A student writes a factoring problem on the chalkboard.

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

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