FACTOR OUT Meaning and
Definition
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Factor out is a term commonly used in mathematics and other similar disciplines and refers to the process of rewriting or transforming an expression or equation by extracting a common factor from its terms. It involves dividing all the terms of an equation or expression by a common factor, resulting in simplification. By factorizing a common factor, the equation or expression can be reduced to a more manageable form, allowing for easier analysis and solving.
In algebra, factor out implies finding the greatest common factor (GCF) of the terms and then dividing each term by this GCF. By doing so, the resulting equation or expression is simplified and can be further manipulated or solved. For instance, given the equation 6x + 9y, the common factor here is 3. Thus, factoring out 3 from each term results in 3(2x + 3y), where 2x + 3y is the simplified form.
The concept of factoring out can also be applied to polynomials, quadratic equations, and more complex mathematical expressions. It aids in simplifying and identifying patterns within equations, therefore enabling easier analysis, solving, or further operations, such as factoring completely or graphing.
Overall, factor out is a fundamental mathematical process aimed at simplifying expressions or equations by dividing all the terms by a common factor. It is a powerful tool in algebraic manipulation, supporting various math operations, problem-solving, and understanding equations.
Common Misspellings for FACTOR OUT
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Etymology of FACTOR OUT
The phrase "factor out" has its roots in mathematics. The term "factor" can be traced back to the Latin word "factor", which means "doer, maker, producer". In mathematics, "factor" refers to a number or expression that divides another number or expression evenly without leaving a remainder.
The word "out" can be traced back to the Old English "ūt", which means "from (a place or time); forth". It is related to the German word "aus".
When these two words are combined in the phrase "factor out", it means to remove or separate a common factor from an expression or equation. This mathematical term is derived from the idea of breaking down an expression into its constituent factors.
Over time, "factor out" has also come to be used in a broader sense, outside of mathematics, to mean isolating or separating a specific element or component from a larger whole.
Idioms with the word FACTOR OUT
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factor out
to separate or isolate a particular factor or element from a larger group or situation
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