The basic guidelines for factoring follow:

- Look to factor out any
**GCF**. **Four-Term Polynomials**- Factor by grouping.**Trinomials**- Factor using the "guess and check" method.**Binomials**- Use the the special products in this order:

**Sum and Difference of Squares**

**Sum and Difference of Cubes**

** If a binomial is both a difference of squares and cubes, then to obtain a more complete factorization, factor it as a difference of squares first.*

** Not all polynomials factor. In this case, beginning algebra students may write, "does not factor - DNF."*

**Factor**.

**Tip**: Make some note cards to aid in helping memorize the formulas for the special products. Look for factors to factor further - sometimes factoring once is not enough.

**Factor**.

*x*^6 -

*y*^6 is both a difference of squares and a difference of cubes at the same time. Here we chose to apply the difference of squares formula first. On the other hand, for

*x*^6 +

*y*^6 we chose to apply the sum of cubes formula first because it does not factor as a sum of squares.

**Factor**.

**Video Examples on YouTube**: Factor the following polynomials.