How to Factor by Grouping in Algebra

By Education Editor

One of the methods of factoring polynomials is to factor by grouping. This method is a basic algebra technique used when other simpler special formulas such as factoring the difference of two cubes or factoring perfect squares do not work.

Look and apply the first rules of factoring by trying to find any common monomial factors in the equation. If the terms do not have one common factor, try factoring by grouping.

Try factoring by grouping if there are more than two or three groups of terms.

Factor polynomials in one variable into products of one variable where all the coefficients are integers otherwise known as factoring over the integers.

Figure out a group of four terms by first grouping the terms of the equation into two groups. Next, factor monomial factors out of each group individually.

Use the following as an example to factor by grouping x^3 - 3x^2 + 2x - 6 = (x^3 - 3x^2) + (2x - 6). Now factor out the common factors from each group such as x^2(x - 3) + 2(x - 3)

Join the common factors that are extracted from each group, as in (x^2 + 2). This applies to all equations in basic algebra that you factor by grouping. The final factored answer is (x^2 + 2)(x - 3)