GeoGebra Classroom

# Finding Things in Common

## OBJECTIVE: To factor out the Greatest Common Factor (GCF) or Common Monomial Factor (CMF) from polynomials

In a previous lesson, you learned about prime factorization of composite numbers using tree diagrams. Climbing Down Trees: https://www.geogebra.org/m/hxmuf2dg In this lesson, you'll learn how to factor out the Greatest Common Factor (GCF) or the Common Monomial Factor (CMF) from polynomials. The easiest, yet the most neglected step in factorization problems, is factoring out the Greatest Common Factor (GCF) or the Common Monomial Factor (CMF). A great deal of factorization problems involve special factors, which remain hidden because of the presence of common factors. Thus, the first step in any factorization problem must be factoring out the GCF or CMF.

## HERE'S HOW ...

1. Determine the greatest common factor of the numerical coefficients for each term. 2. Determine the smallest power of each variable common to all terms, and multiply this by the common factor from step 1 to complete the GCF. 3. Write expressions for the remaining non-common factors. 4. Verify the result using the Distributive Property. The applet below illustrates the process.

## Practice some more with the applet below.

Repeat as many times as needed to master the concept.

## Applet 2 by Walch Education

Below is a set of problems that require you to factor out the Greatest Common Factors (GCF) from polynomials. Write your solutions and answers on a separate sheet of paper. Then check the Answer Box below for the correct answers.