Factoring Polynomials by Finding the Greatest Common
Factor (GCF)
Factoring Out the Greatest Common Factor (GCF) of a Polynomial
Procedure â€”
To Factor Out the GCF of a Polynomial
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 Write as a product using the GCF.
If there is no factor, other than 1, common to each term, then the
GCF is 1.
Example 2
Factor: 42w^{2}y^{2}  28w^{3}y^{2} + 14wy^{3}.
Solution
Step 1 Identify the terms.
Step 2 Factor each term. 
42w^{2}y^{2}, 28w^{3}y^{2},
14wy^{3}
42w^{2}y^{2} = 2 Â· 3
Â· 7 Â· w
Â· w Â· y
Â· y
28w^{3}y^{2} = 1 Â· 2
Â· 2 Â· 7
Â· w Â· w
Â· w Â· y
Â· y
14wy^{3} = 2 Â· 7
Â· w Â·
y Â· y Â·
y 
Step 3 Find the GCF of the terms.
In the lists, the common factors are 2, 7, w, y, and y.
Therefore, the GCF is 2 Â· 7
Â· w Â·
y Â· y = 14wy^{2}.
Step 4 Rewrite each term using the GCF. 
Original trinomial.
Rewrite each term
using the GCF. 
42w^{2}y^{2}  28w^{3}y^{2} + 14wy^{3}
= 14wy^{2} Â· 3w  14wy^{2}
Â· 2w^{2} + 14wy^{2} Â·
y 
Step 5 Write as a product
using the GCF. 
= 14wy^{2}(3w  2w^{2} + y) 
So, the factorization is 14wy^{2}(3w  2w^{2} + y).
Note:
We can multiply to check the factorization.
14wy^{2}(3w  2w^{2} + y)
= 14wy^{2} Â· 3w  14wy^{2}
Â· 2w^{2} + 14wy^{2} Â·
y
= 42w^{2}y^{2}  28w^{3}y^{2} + 14wy^{3}
