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# Factoring Polynomials

## Factoring a Polynomial Whose GCF is a Binomial

You have already seen how to factor a polynomial when the GCF of the terms is a monomial.

In this example, we factor out the monomial 2x.

10x2 + 8x

= 2x Â· 5x + 2x Â· 4

= 2x(5x + 4)

We can also factor a polynomial when the GCF of its terms is a binomial.

 Here, the binomial (x + 7) is a factor of each term. So we factor out (x + 7). = 5x(x + 7) + 4(x + 7)  = (x + 7)(5x + 4)

Example 1

Factor: 2m(6n - 5) - 7(6n - 5)

Solution

 The GCF of the terms is the binomial (6n - 5). Factor out the GCF. 2m(6n - 5) - 7(6n - 5) = (6n - 5)(2m - 7)