


The ProcessFactoring completely is a three step process:
First ExampleLet's see how this applies to our initial example: (x^{4}  1) Step 1Step one is to factor a GCF. Since the GCF of x^{4} and 1 is 1, we skip this step. Step 2Since the expression only has two terms, we cannot factor a trinomial. Step 3Factoring (x^{4}  1) as a difference between two squares results in (x^{2} + 1)(x^{2}  1). Now be sure to remember the key phrase "as many times as possible." We must now look to see if there is anywhere else we can factor another Difference Between Two Squares. In (x^{2} + 1), both terms are positive, so this cannot be factored. However, in (x^{2}  1), the second term is negative, and both terms are perfect squares otherwise. So (x^{2}  1) factors into (x + 1)(x  1). As a result, our example expression is finally factored into (x^{2} + 1)(x + 1)(x  1) which is factored completely. How did this differ from our first (and failed) attempt to factor the example? When Factoring Completely, we used the Difference Between Two Squares method more than once. Proceed to the next page for another example. 

