EDGE Math 8

Common Monomial Factoring

The common monomial factoring technique is based on the following property:

a x + a y = a (x + y) .

There are two steps in this technique. The first step involves finding the greatest common monomial factor of the terms of the given polynomial. The second step is to find the remaining factor by dividing the given polynomial by the greatest common monomial factor.

For example, to find the greatest common monomial factor of $6 b^{3} + 9 b^{2},$ consider the numerical coefficients 6 and 9 first. These numbers have 3 as their GCF. Next, consider the literal coefficients $b^{3}$ and $b^{2}$ . Their GCF is $b^{2}$ . Thus, the greatest common monomial factor of $6 b^{3} + 9 b^{2}$ is $3 b^{2} .$

Next, find the second factor. Divide each term of $6 b^{3} + 9 b^{2}$ by $3 b^{2} .$ This yields $\frac{6 b^{3}}{3 b^{2}} + \frac{9 b^{2}}{3 b^{2}} = 2 b + 3.$ Thus, the factors of $6 b^{3} + 9 b^{2}$ are the monomial $3 b^{2}$ and the prime polynomial $2 b + 3.$ Its factored form can be written as

6 b^{3} + 9 b^{2} = 3 b^{2} (2 b + 3) .