Trial and Error Examples Page 2

Factor the polynomial 2x³ - 8x² + 6x.

This polynomial isn't quadratic. However, all the terms have a common factor of 2x. Let's take that out and see what happens. First:

(2x)(x² - 4x + 3).

The second factor is quadratic. Can we factor it further? We need two numbers whose product is 3 and whose sum is -4. Hey, we happen to know the two numbers that will fit the bill. -3 and -1 work, so we can factor the original polynomial as

(2x)(x - 3)(x - 1).

Remember, you can always check your answer to a factoring problem by multiplying out the factors. The product of the factors should be the original polynomial. If it isn't, you've gone wrong somewhere. Maybe you took a wrong turn at Algebraquerque.