Factor by grouping

Definition

Factor by grouping is a method used to factor polynomials that involves rearranging and combining terms into groups that have a common factor. This technique is particularly useful for polynomials with four or more terms.

5 Must Know Facts For Your Next Test

1. Factor by grouping works best when the polynomial has an even number of terms, typically four.
2. The first step is to split the polynomial into two groups and then factor out the greatest common factor (GCF) from each group.
3. After factoring out the GCF from each group, check if the remaining binomials are identical.
4. If the binomials are identical, they can be factored out as a common term, resulting in a product of two binomials.
5. If the binomials are not identical after grouping and factoring, recheck your initial groupings or consider other factoring techniques.

Review Questions

• What is the first step in factoring by grouping?
• How do you determine if your grouping was successful?
• What should you do if the binomials after factoring are not identical?

Related terms

Greatest Common Factor (GCF):

The largest factor that divides two or more numbers or terms without leaving a remainder.

Binomial:

A polynomial with exactly two terms separated by a plus or minus sign.

Polynomial:

\text{An algebraic expression consisting of variables and coefficients, composed using addition, subtraction, multiplication, and non-negative integer exponents.}