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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.

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A simple version of the factoring strategy is given below. 1.Always factor the Greatest Common Factor first. 2.Determine how many terms are left in the resulting polynomial. 3.Factor using the methods for that number of terms. 4.After completing a step, always ask, can I factor again? This is best described in the following diagram.

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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. Dont forget the GCF!

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

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

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

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

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

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

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

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

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

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

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

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

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Any more factoring possible?No

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

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

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

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