Factor by grouping

Definition

Factor by grouping is a method used to factor polynomials that involve grouping terms with common factors and then factoring out the greatest common factor from each group. This technique is particularly useful for polynomials with four or more terms.

5 Must Know Facts For Your Next Test

1. Factor by grouping is typically used when a polynomial has four terms.
2. The first step in factoring by grouping is to group the terms into pairs.
3. After grouping, you factor out the greatest common factor (GCF) from each pair of terms.
4. If done correctly, the remaining binomials should have a common binomial factor that can be factored out.
5. The final factored form should be a product of two binomials or other simpler polynomials.

Review Questions

• What initial step must you take when using the factor by grouping method?
• How do you determine which terms to group together in the factor by grouping method?
• What indicates that you have successfully factored a polynomial using the factor by grouping method?

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, typically connected by a plus or minus sign.

Polynomial: An algebraic expression made up of one or more terms, where each term includes a variable raised to an exponent and has a coefficient.