Factoring – General Method You have learned a variety of methods for factoring. This section puts all of the methods together for a general factoring strategy. It is very important that you can factor a polynomial without being told what method to use. In fact, sometimes several methods will be used on the same problem.

A simple version of the factoring strategy is given below. Always factor the Greatest Common Factor first. Determine how many terms are left in the resulting polynomial. Factor using the methods for that number of terms. After completing a step, always ask, can I factor again? This is best described in the following diagram.

Greatest Common Factor The Greatest Common Factor is always the first step in factoring. If you leave this step out, the factoring can get extremely difficult or impossible. Don’t forget the GCF!

Greatest Common Factor Two Three Four How many terms are there? The number of terms determines the possible methods to consider.

Greatest Common Factor Two Three Four Difference of Two Squares Lets start with two terms. Sum of Two Cubes The possible factoring methods include … Difference of Two Cubes

Greatest Common Factor Two Three Four Difference of Two Squares Perfect Square Trinomial If there are three terms. Sum of Two Cubes Trinomial: Guess/Check or ac Method Difference of Two Cubes

Greatest Common Factor Two Three Four Difference of Two Squares Perfect Square Trinomial Grouping Sum of Two Cubes Trinomial: Guess/Check or ac Method If there are four terms. Difference of Two Cubes

Example 1 Factor: Factor the GCF Two terms are left in the resulting polynomial

Greatest Common Factor Two Three Four Difference of Two Squares Perfect Square Trinomial Grouping Sum of Two Cubes Trinomial: Guess/Check or ac Method Difference of Two Cubes

Greatest Common Factor Two Difference of Two Squares Sum of Two Cubes Consider these three methods Difference of Two Cubes

Example 1 Factor: Factor the GCF Two terms are left in the resulting polynomial It’s a difference of two squares. Any more factoring possible? No

Example 2 Factor: Factor the GCF Three terms are left in the resulting polynomial

Greatest Common Factor Two Three Four Difference of Two Squares Perfect Square Trinomial Grouping Sum of Two Cubes Trinomial: Guess/Check or ac Method Difference of Two Cubes

Greatest Common Factor Three Perfect Square Trinomial Check for a Perfect Square Trinomial first Trinomial: Guess/Check or ac Method

Example 2 Factor: Factor the GCF Three terms are left in the resulting polynomial It is a perfect square trinomial.

Any more factoring possible? No

Example 3 Factor: Factor the GCF None, other than 1 Four terms suggests the grouping method.

Any more factoring possible? Yes, a difference of two squares. Any more factoring possible? No

With factoring it is important to remember, after completing a factoring step, always ask Is there any more factoring possible?

END OF PRESENTATION