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# Factoring a Polynomial by Finding the GCF

To factor a polynomial such as 6wx2 + 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: 6x2 + 8xy2 - 2x

Solution

 Step 1 Identify the terms of the polynomial. 6x2, 8xy2, Step 2 Factor each term. 6x2 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. = 6x2 + 8xy2 - 2x6x2 + 8xy2 + (- 2x) Rewrite each term using 2x as a factor. = 2x Â· 3x + 2x Â· 4y2 + 2x Â· (-1) Step 5 Factor out the GCF. Factor out 2x. = 2x(3x + 4y2 -1)
Thus, 6x2 + 8xy2 - 2x = 2x(3x + 4y2 - 1)

We can multiply to check the factorization. We use the distributive property.

 IsIs Is 2x(3x + 4y2 -1)2x Â· 3x + 2x Â· 4y2 + 2x Â· (-1) 6x2 + 8xy2 - 2x 6x2 + 8xy2 - 2x ?6x2 + 8xy2 - 2x ? 6x2 + 8xy2 - 2x ? Yes