To attempt to factor a polynomial of four or more terms with no common factor, first rewrite it in groups. Each group may then be separately factored, and the resulting expression may lend itself to further factorization.
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
So
Example 2: Factor
x2 + 2
xy +
y2 −
z2.
This polynomial has four terms with no common factor. Also notice that
Example 3: Factor
x2 −
y2 +
x3 +
y3
Linear Sentences in One Variable
Factoring Polynomials
