# Complete Factoring

When factoring an expression, first check for a common factor, then check for a difference of squares, then for a perfect square trinomial, and then for a general trinomial.

Example

*Factor the expression 2x ^{3} â€“ 2x^{2} â€“ 12x completely.*

Solution: First check for a common factor: 2*x* is common to each term. Factoring 2*x* out of each term yields 2*x*(*x*^{2} â€“ *x* â€“ 6).

Next, there is no difference of squares, and *x*^{2} â€“ *x* â€“ 6 is not a perfect square trinomial since *x* does not equal twice the product of the square roots of *x*^{2} and 6.

Now, â€“3 and 2 are factors of â€“6 whose sum is â€“1.

Hence, 2*x*(*x*^{2} â€“ *x* â€“ 6) factors into 2*x*(*x* â€“ 3)(*x* + 2).