Factoring by Regrouping

To attempt to factor a polynomial of four or more terms with no common factor, first rewrite it in groups. Each group may possibly be separately factored, and the resulting expression may possibly lend itself to further factorization if a greatest common factor or special form is created.

Example 1

Factor ay + az + by + bz.

This polynomial has four terms with no common factor. It could be put into either two groups of two terms or two groups with three terms in one group and one term in the other group. One such arrangement is equation

So equation

The two new terms have a GCF of y + z.

Example 2

Factor x 2 + 2 xy + y 2z 2.

This polynomial has four terms with no common factor. Also notice that equation

Example 3

Factor x 2y 2 + x 3 + y 3

equation