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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 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 + y2z2.

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




Example 3: Factor x2y2 + x3 + y3




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