Factoring a Polynomial by Finding the GCF
To factor a polynomial such as 6wx^{2} + 18wxy + 3wx + 9wy, we may
need to use several factoring techniques.
The first step is to factor out the GCF of the monomial terms.
Procedure â€”
To Factor Out the GCF of a Polynomials
Step 1 Identify the terms of the polynomial.
Step 2 Factor each term.
Step 3 Find the GCF of the terms.
Step 4 Rewrite each term using the GCF.
Step 5 Factor out the GCF.
If there is no factor (other than 1) common to each term, the GCF is 1.
To check the factorization, multiply the factors.
Example 1
Factor: 6x^{2} + 8xy^{2}  2x
Solution
Step 1 Identify the terms of the polynomial.

6x^{2}, 8xy^{2}, 
Step 2 Factor each term. 
6x^{2}
8xy
2x 
= 2
Â· 3 Â· x Â· x
= 2
Â· 2 Â· 2 Â· x Â· y Â· y
= 1 Â· 2 Â· x 
Step 3 Find the GCF of the terms.
In the lists, the common factors are 2 and x.
The greatest common factor (GCF) is 2 Â· x
= 2x.
Step 4 Rewrite each term using the GCF. 


To help keep the signs straight, write the
subtraction of 2x as the addition of 2x. 
= 
6x^{2} + 8xy^{2}  2x 6x^{2} + 8xy^{2}
+ ( 2x) 
Rewrite each term using 2x as
a factor. 
= 
2x Â· 3x +
2x Â· 4y^{2} + 2x Â· (1) 
Step 5 Factor out the GCF.
Factor out 2x. 
= 
2x(3x + 4y^{2} 1) 
Thus, 6x^{2} + 8xy^{2}  2x = 2x(3x + 4y^{2}  1)
We can multiply to check the factorization. We use the distributive
property.
Is Is
Is 
2x(3x + 4y^{2} 1) 2x Â· 3x +
2x Â· 4y^{2} + 2x Â· (1)
6x^{2} + 8xy^{2}  2x 
6x^{2} + 8xy^{2}  2x ? 6x^{2} + 8xy^{2}  2x
?
6x^{2} + 8xy^{2}  2x ? Yes 
