I recently finished another squidoo lens on working with polynomials. One of the goals of the lens is to teach students how to factor quadratic expressions. I was taught the guess and check method to factor quadratics and have always held the belief this was the best method to factor quadratic expressions. One of my fundamental theories on math education is the importance of teaching the why along with the how. The guess and check method may not always be the easiest "how" but I have always thought it was the best "why".
I will confess I have not worked much with the other more algorithmic methods of factoring quadratic expressions. If you teach/use this method, I would love to hear why you think it is the best way to teach the concept?