Determine that there is no greater common factor to simplify the problem. For example, the problem f(x)= 9x^2 + 30x + 25 does not have any common factors because there is no single factor that can be pulled out of all three pieces.
Break each piece up into its own factors. For f(x)= 9x^2 + 30x + 25 this looks like f(x)= (3x)^2 + 2(3x)(5) + (5)^2. Once broken down into this form, it matches the Perfect Square Trinomial Rule of a^2 + 2ab + b^2 = (a+b)^2.
Write out the factored result using the rule. For the example, the final result is (3x+5)^2.