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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# 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: 42w2y2 - 28w3y2 + 14wy3.

Solution

 Step 1 Identify the terms. Step 2 Factor each term. 42w2y2, -28w3y2, 14wy3 42w2y2 = 2 Â· 3 Â· 7 Â· w Â· w Â· y Â· y -28w3y2 = -1 Â· 2 Â· 2 Â· 7 Â· w Â· w Â· w Â· y Â· y 14wy3 = 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 = 14wy2. Step 4 Rewrite each term using the GCF. Original trinomial. Rewrite each term using the GCF. 42w2y2 - 28w3y2 + 14wy3 = 14wy2 Â· 3w - 14wy2 Â· 2w2 + 14wy2 Â· 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 Â· 3w - 14wy2 Â· 2w2 + 14wy2 Â· y

= 42w2y2 - 28w3y2 + 14wy3