For example, 4 x^2 + 12x + 9 factors to (2x + 3)^2 , and a^2 − 10a + 25 factors to (a − 5)^2.
Sometimes you’ll want to factor a polynomial that’s not in any of these classic factorable forms.
When that happens, factoring becomes a kind of logic exercise, with some trial and error thrown in.
To factor a quadratic expression, think about what binomials you could use FOIL on to get that
quadratic expression. For example, to factor x^2 − 5x + 6, think about what First terms will produce x^2 ,
what Last terms will produce +6, and what Outer and Inner terms will produce −5x. Some common
sense—and a little trial and error—will lead you to (x − 2)(x − 3).
Example 4 is a good instance of a Math 2 question that calls for factoring.
Example 4To reduce a fraction, you need to eliminate common factors from the top and the bottom. This is
just as true for algebraic equations as it is for integers. The first step should be to try and simplify the
numerator or denominator, which will help in factoring. Notice that 3 is a factor of every term in the
numerator:
Next, factor both the numerator and denominator:
1. For all