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 · 5x + 2x
· 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) |