Factoring by Grouping

Factoring by grouping is a method used to factor polynomials that have four terms. The method involves grouping pairs of terms and factoring out the greatest common factor from each pair.

Steps for Factoring by Grouping

1. Group the terms: Arrange the terms of the polynomial into two pairs.
2. Factor out the GCF: Factor out the greatest common factor from each pair of terms.
3. Factor out a common binomial factor: Factor out the common binomial factor from the grouped terms.
4. Check for further factorization: Look for opportunities to factor the resulting quadratic expression further, if possible.

Example

Let's factor the polynomial 2x + 6 + 3x + 9 by grouping:

Step 1: Group the terms

Step 2: Factor out the GCF from each pair

Step 3: Factor out the common binomial factor

Step 4: Further factorization (if possible)

Study Guide

Here are some key points to remember when factoring by grouping:

• Make sure the polynomial has four terms before using the factoring by grouping method.
• Look for common factors within each pair of terms and factor them out first.
• Pay attention to the signs when factoring out the greatest common factor from each pair.
• Always check to see if the resulting expression can be further factored after grouping.

Practice factoring by grouping with various examples to master this technique.