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Algebra Homework Help : Finding the GCF in Algebraic Terms

 
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How to Find the GCF in Two or More Algebraic Terms ?

Finding the Greatest Common Factor (GCF) in two or more algebraic terms involves three steps:
1. Find the GCF of all the coefficients (numbers).
2. Find the GCF of all the variables (letters) by taking each variable to its lowest exponent.
3. Write the GCF of the terms as the product of the GCF of the coefficients and the GCF of the variables.

 

Example 1. GCF of 8x4, 4x2 and 12x is 4x.
Here, the GCF of the coefficients (8, 4 and 12) is 4.
The GCF of the variables (x4, x2 and x) is x (i.e., the variable raised to the lowest exponent).
The GCF of the terms 8x4, 4x2 and 12x is 4x (i.e., the product of 4 and x).

 

Example 2. GCF of 27ab3 and 18a2b2 is 9ab2.
Here, the GCF of the coefficients (27 and 18) is 9.
The GCF of the variables (ab3 and a2b2) is ab2 (i.e., each variable with its lowest exponent).
The GCF of the terms 27ab3 and 18a2b2 is 9ab2 (i.e., the product of 9 and ab2).

 

Note that a variable having an exponent of one is written without an exponent (i.e., x1 = x) and a variable with an exponent of zero equals one (i.e., x0 = 1).


 Practice Exercise for Algebra Module on Finding GCF in Algebraic Terms

 

 
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