How to pull out the greatest common factor of polynomials

The key is that all the terms of the polynomial need to share the factor being taken out. Any factor that’s shared by all the terms is called a common factor, and the factor that consists of everything which is shared by all of them is known as the greatest common factor. Factoring is “un-distributing,” which means that we do the opposite of distributing and take out (or “factor out”) the same factor from each term of the polynomial (and divide each term by that factor to get “what’s left” once it’s taken out).

Finding the greatest common factor of a pair or set of numbers

A common factor of two positive whole numbers is a number that divides evenly into both of them. Their greatest common factor (sometimes abbreviated GCF) is the largest number that divides evenly into both of them. Another name that’s used for “greatest common factor” is “greatest common divisor” (sometimes abbreviated GCD).

Factoring out the greatest common factor from trinomials

The key to factoring is that every term in the trinomial needs to share the factor being taken out. Any factor that’s shared by all the terms is called a common factor, and the factor that consists of everything which is shared by all of them is known as the greatest common factor.

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