key term - Factor by Grouping

Definition

Factoring by grouping is a technique used to factor polynomials by identifying common factors among groups of terms within the polynomial. This method involves dividing the polynomial into smaller groups, finding the common factor of each group, and then factoring out that common factor to simplify the expression.

5 Must Know Facts For Your Next Test

1. Factoring by grouping is particularly useful when dealing with polynomials that have four or more terms.
2. The first step in factoring by grouping is to divide the polynomial into two or more groups, based on the common factors present.
3. Once the groups are identified, the common factor of each group is found and factored out, leaving a simpler expression to work with.
4. Factoring by grouping can reveal the greatest common factor (GCF) of the entire polynomial expression.
5. This technique can be applied to both binomials and trinomials, as long as there are at least four terms in the polynomial.

Review Questions

• Explain the process of factoring by grouping, including the steps involved.
  • The process of factoring by grouping involves the following steps: 1) Divide the polynomial expression into two or more groups based on the common factors present. 2) Find the common factor of each group. 3) Factor out the common factor from each group, leaving a simpler expression. 4) Combine the factored groups using the distributive property to obtain the final factored form of the polynomial.
• Describe the advantages of using the factoring by grouping method compared to other factoring techniques.
  • The main advantage of factoring by grouping is that it can be used to factor polynomials with four or more terms, which may not be easily factored using other methods like the greatest common factor (GCF) or the difference of two squares. Factoring by grouping can reveal the GCF of the entire polynomial, making it a versatile and powerful factoring technique. Additionally, it can be applied to both binomials and trinomials, providing a flexible approach to factoring various polynomial expressions.
• Analyze the role of common factors in the factoring by grouping method and explain how identifying these factors simplifies the factorization process.
  • The identification of common factors is crucial in the factoring by grouping method. By dividing the polynomial into groups based on the common factors present, the factorization process is significantly simplified. Finding the common factor of each group and factoring it out leaves a simpler expression to work with, making it easier to identify and factor out additional common factors. This step-by-step approach of isolating and factoring out common factors ultimately leads to the fully factored form of the original polynomial expression.

Related terms

Factoring:

The process of breaking down a polynomial expression into a product of simpler polynomial expressions.

Common Factor: A factor that is shared by two or more terms in a polynomial expression.

Polynomial:

An algebraic expression consisting of variables and coefficients, where the variables are only raised to non-negative integer powers.