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.

Noun

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