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

Group the terms: Arrange the terms of the polynomial into two pairs.
Factor out the GCF: Factor out the greatest common factor from each pair of terms.
Factor out a common binomial factor: Factor out the common binomial factor from the grouped terms.
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

2x + 6 + 3x + 9

Step 2: Factor out the GCF from each pair

2x + 6 = 2(x + 3) 3x + 9 = 3(x + 3)

Step 3: Factor out the common binomial factor

2(x + 3) + 3(x + 3) = (x + 3)(2 + 3) = (x + 3)(5)

Step 4: Further factorization (if possible)

The resulting expression (x + 3)(5) is already fully factored.

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.

◂Math Worksheets and Study Guides Sixth Grade. Plotting Points

Vocabulary/Answer key

Plotting Points

The resources above cover the following skills:

The Number System

Apply and extend previous understandings of numbers to the system of rational numbers.

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. [6-NS6]

Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. [6-NS6b]

Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. [6-NS6c]

Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. [6-NS8]