Factoring: meaning, definitions and examples
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factoring
[ ˈfæktərɪŋ ]
mathematics education
Factoring involves breaking down an expression into its multiplicative components. It is a fundamental process in algebra that allows for simplification of expressions and solving equations. Factoring can be applied to polynomials, where the goal is to express the polynomial as a product of simpler polynomials. This technique is essential for solving quadratic equations and understanding the behavior of functions. Mastery of factoring is crucial for higher-level mathematics.
Synonyms
breaking down, decomposition, simplification.
Examples of usage
- Factoring the quadratic equation helps find its roots.
- In mathematics class, we learned about factoring polynomials.
- Factoring can simplify complex math problems.
- She excelled in factoring expressions in her algebra homework.
Etymology
The term 'factoring' comes from the Latin word 'facere,' which means 'to do' or 'to make.' The process of factoring has been an integral part of mathematics for centuries, evolving from early arithmetic and algebraic techniques. The modern use of the term developed alongside the formalization of algebra in the 17th century, when mathematicians began to study polynomials in greater depth. Factoring techniques allow mathematicians to analyze and simplify mathematical expressions effectively, establishing a foundation for solving equations and analyzing relationships between numbers. The concept of breaking down mathematical entities into simpler forms has continued to evolve, with significant contributions from various cultures, including the Greeks and Arabs, which have shaped contemporary algebraic practices.