Factorability: meaning, definitions and examples
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factorability
[ ˌfæktəˈrəbility ]
mathematics concept
Factorability refers to the property of a mathematical expression or number that signifies it can be expressed as a product of other factors. In algebra, a polynomial is said to be factorable if it can be written as a product of simpler polynomials. Generally, the notion of factorability is significant in solving equations and simplifying expressions.
Synonyms
decomposition, factorization.
Examples of usage
- The factorability of the quadratic polynomial made it easier to solve.
- Understanding the factorability of expressions is crucial for algebra students.
- Not all numbers show factorability; for instance, prime numbers cannot be factored apart from one and themselves.
Etymology
The word 'factorability' is derived from the root 'factor', which originates from the Latin word 'factorem', meaning 'maker' or 'doer'. The suffix '-ability' indicates the quality of being able to do something. This formation reflects how the concept of factorability is fundamental in mathematics, especially in algebra, where expressions are manipulated and simplified. The use of 'factor' in English dates back to the late 14th century, primarily in the context of commerce, referring to someone who acts on behalf of another. As mathematics evolved, the term adapted to describe the process of breaking down numbers or expressions into their component parts, leading to the modern conception of factorability seen in contemporary algebra and number theory.