Factor common to all terms:ax + ay = a(x + y)Difference of squares:a^2 – b^2 = (a – b)(a + b)Square of binomial:a^2 + 2ab + b^2 = (a + b)^2Sometimes 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 1 question that calls for factoring.
Example 41. For all x ≠ ±3,