Factor Using the Greatest Common Factor
When factoring, you should ALWAYS check for a greatest common factor first! The greatest common factor (or GCF) is the largest factor that all terms have in common.
Here are some steps to follow when factoring using the greatest common factor:
You can check that you have factored correctly by using the distributive property.
Here is an example:
Here are some steps to follow when factoring using the greatest common factor:
- Find the GCF of ALL terms (include both numbers and variables)
- Write the GCF and make parentheses
- Divide every term in the original polynomial by the GCF and write that quotient inside the parentheses (remember the Quotient of Powers Property)
You can check that you have factored correctly by using the distributive property.
Here is an example:
Step 1: Find the GCF
Looking at the numbers, the GCF of 6, 18, and 9 is 3
Looking at the variables, the largest number of x's that we can take out of each term is two
Therefore, our GCF is:
Looking at the numbers, the GCF of 6, 18, and 9 is 3
Looking at the variables, the largest number of x's that we can take out of each term is two
Therefore, our GCF is:
Step 2: Write the GCF and make parentheses
Step 3: Divide every term by the GCF and write the quotient inside the parentheses
Check by distributing:
Watch the following video to see more examples of factoring using the GCF. Notice that these examples have more than one variable.
Factoring Using the Greatest Common Factor, GCF - Example 1 by patrickJMT: https://www.youtube.com/watch?v=3RJlPvX-3vg
Practice:
Check out this website for extra practice finding the GCF with a single variable:
https://www.ixl.com/math/algebra-2/factor-monomials
Check out this website for extra practice finding the GCF with more than one variable:
http://www.mesacc.edu/~scotz47781/mat120/notes/factoring/gcf/gcf_practice.html
https://www.ixl.com/math/algebra-2/factor-monomials
Check out this website for extra practice finding the GCF with more than one variable:
http://www.mesacc.edu/~scotz47781/mat120/notes/factoring/gcf/gcf_practice.html
Quick Check:
Complete the following quick check. When you are finished (and have mastered) the greatest common factor, move onto "Difference of Squares."
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