


Second ExampleLet's try another example which requires factoring in steps 1 and 2: 5x^{3}  10x^{2}  15x Again, the three steps in Factoring Completely are:
Step 1We see that the terms in our example have a greatest common factor of 5x. As instructed, we will factor out this GCF: 5x(x^{2}  2x  3) Step 2We see that (x^{2}  2x  3) is a factorable trinomial, so we factor it: 5x(x + 1)(x  3) Proceeding to Step 3, we can look over our expression and see that neither 5x, nor (x + 1), nor (x  3) can be factored as a difference between two squares. We have factored 5x^{3}  10x^{2}  15x completely. Final ExampleFor our final example, we will make use of all three Factoring Completely steps. 12x^{4}  3x^{2}  54 Step 1We factor out a Greatest Common Factor of 3. 3(4x^{4}  x^{2}  18) Step 23(4x^{2}  9)(x^{2} + 2) Step 3Finally, we identify (4x^{2}  9) as a binomial that can be factored into (2x + 3)(2x  3). So the completely factored result is 3(2x + 3)(2x  3)(x^{2} + 2). 

