Finding Things in Common

What do they have in common?
OBJECTIVE: To factor out the Greatest Common Factor (GCF) or Common Monomial Factor (CMF) from polynomials
[br]In a previous lesson, you learned about [color=#0000ff]prime factorization[/color] of composite numbers using [color=#0000ff]tree diagrams[/color].[br][br][color=#0000ff][i]Climbing Down Trees:[/i][/color] https://www.geogebra.org/m/hxmuf2dg[br][br]In this lesson, you'll learn how to factor out the [color=#0000ff]Greatest Common Factor (GCF)[/color] or the [color=#0000ff]Common Monomial Factor (CMF) [/color]from polynomials.[br][br]The easiest, yet the most neglected step in factorization problems, is factoring out the [color=#0000ff]Greatest Common Factor (GCF) [/color]or the [color=#0000ff]Common Monomial Factor (CMF). [/color]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 [color=#0000ff]GCF[/color] or [color=#0000ff]CMF.[/color]
HERE'S HOW ...
[br]1. Determine the greatest common factor of the numerical coefficients for each term.[br][br]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.[br][br]3. Write expressions for the remaining non-common factors.[br][br]4. Verify the result using the [color=#0000ff]Distributive Property[/color].[br][br]The applet below illustrates the process.
Applet 1 by Walch Education
Practice some more with the applet below.
[br]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.[br][br]Write your solutions and answers on a separate sheet of paper. Then check the Answer Box below for the correct answers.
Greatest Common Factor
ANSWER BOX:
[br]Check out the answers to the above problems here. [br][br]
TODAY you learned how to factor out the Greatest Common Factor (GCF) or Common Monomial Factor (CMF) from polynomials.
In future lessons, you'll learn how to work on special factors. Did you have FUN in today's lesson?
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– Jaime Dianzon

Information: Finding Things in Common