factor out

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Definition
  1. Verb (transitive):
    • To remove a common factor from an expression: In mathematics, to rewrite an expression by taking a common element (a number, variable, or term) out of each part, often placing it outside parentheses.
    • To exclude or leave out as a consideration: To deliberately not include a particular element, variable, or influence when analyzing a situation or making a calculation.
Usage
  • Mathematical Usage: The verb is used when simplifying algebraic expressions or equations by identifying and extracting a common multiplier.
  • Analytical/Decision-Making Usage: The verb is used to indicate the act of isolating or disregarding a specific factor to assess the impact of other variables or to simplify an analysis.
Examples
  • Mathematical Context:
    • To simplify the equation, you can factor out the common variable 'x'.
    • The expression 6y + 9 can be rewritten by factoring out the number 3, resulting in 3(2y + 3).
  • Analytical Context:
    • When comparing the two companies' performance, we should factor out the effect of last year's one-time tax benefit.
    • To understand the true trend, the economist factored out seasonal variations from the employment data.
Advanced Usage
  • "to factor something out of something": This structure specifies both the element being removed and the subject from which it is removed.
    • The researcher factored the anomalous data points out of the final analysis.
Variants and Related Words
  • Factor (verb): To include or consider as a relevant element. (e.g., )
  • Factorization / Factorisation (noun): The process of breaking down a number or expression into factors.
  • Common factor (noun): A number or expression that divides exactly into two or more given numbers or expressions.
Synonyms
  • Mathematical: Extract, remove (a common factor).
  • Analytical: Exclude, disregard, isolate, omit, screen out.
Related Phrasal Verbs
  • Factor in: The direct opposite in analytical contexts, meaning to include something as a relevant element in a decision or calculation.
    • Be sure to factor in travel time when planning your day.
Notes on Meaning

The meaning of "factor out" is highly dependent on context. In mathematics, it is a precise technical term. In general analysis, it means to consciously exclude an influence to see the remaining components more clearly. It does not mean to resolve into all possible factors (which is simply "to factor").

Verb
  1. resolve into factors
    • a quantum computer can factor the number 15
  2. consider as relevant when making a decision
    • You must factor in the recent developments

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