What does factorized mean?
Factorized is the past tense of factorize, a verb rooted in mathematics that means to express a quantity as a product of its factors. When an integer is factorized, it is broken into numbers that multiply together to give the original — most usefully into primes, since every integer above 1 has exactly one such decomposition. When a polynomial is factorized, it is rewritten as a product of simpler expressions, such as turning x² − 9 into (x + 3)(x − 3), a step that often makes equations far easier to solve. The word also sees extended, figurative use beyond mathematics: analysts may say they factorized a problem when they separated it into its underlying causes or components. The tone is precise and technical, and the term pairs naturally with words like fully and form, as in a fully factorized expression. Its counterpart operation, expansion or multiplying out, reverses the process.
verbPast tense and past participle of "factorize": to express a number, polynomial, or other mathematical expression as a product of its factors. More generally, to break something down into its constituent components or factors.
- To express a number as a product of its prime or constituent factors.
- To rewrite a polynomial or algebraic expression as a product of simpler expressions.
- (Extended use) To analyze or break down a complex situation into its underlying components.
"The quadratic was factorized into two linear terms."
"She factorized the expression x² − 9 as (x + 3)(x − 3)."
"The consultant factorized the company's declining revenue into pricing, volume, and market-share effects."
Every whole number greater than 1 has exactly one prime factorization — which is why mathematicians call it the 'fundamental theorem of arithmetic' and why breaking a number down never gives two different answers.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of factorized
The word derives from "factor," which comes from Latin factor, meaning "maker" or "doer," from facere, "to do or make." The mathematical sense of factor as a component of a product developed in English by the early modern period, and factorize emerged as a verb form in the nineteenth century alongside related coinages like factorial. The same Latin root gave English factory, manufacture, and fact — all carrying some sense of making or doing.
Related word forms
How factorized is actually used
"Factorize" is the standard spelling in American English, while "factorise" is common in British English; the meaning is identical. The term belongs primarily to mathematics, so extended figurative uses carry a slightly technical, analytical tone.
Easily confused with factorized
"Rationalized" means freed of irrational terms or given rational justification, while "factorized" specifically means rewritten as a product of factors.