Factoring Polynomials by Finding the Greatest Common
Factor (GCF)
Factoring Out the Greatest Common Factor (GCF) of a Polynomial
Procedure —
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: 42w2y2 - 28w3y2 + 14wy3.
Solution
| Step 1 Identify the terms.
Step 2 Factor each term. |
42w2y2, -28w3y2,
14wy3
42w2y2 = 2 · 3
· 7 · w
· w · y
· y
-28w3y2 = -1 · 2
· 2 · 7
· w · w
· w · y
· y
14wy3 = 2 · 7
· w ·
y · y ·
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 · 7
· w ·
y · y = 14wy2.
Step 4 Rewrite each term using the GCF. |
| Original trinomial.
Rewrite each term
using the GCF. |
42w2y2 - 28w3y2 + 14wy3
= 14wy2 · 3w - 14wy2
· 2w2 + 14wy2 ·
y |
| Step 5 Write as a product
using the GCF. |
= 14wy2(3w - 2w2 + y) |
So, the factorization is 14wy2(3w - 2w2 + y).
Note:
We can multiply to check the factorization.
14wy2(3w - 2w2 + y)
= 14wy2 · 3w - 14wy2
· 2w2 + 14wy2 ·
y
= 42w2y2 - 28w3y2 + 14wy3
|
