Question 310685: Under what circumstances would prefer using factoring, completing the square and quadratic formula over each other? Answer by solver91311(24713) (Show Source):
Factoring is very handy for quadratics that are easily factored. If you don't see the factorization right off, do a quick mental calculation of the Discriminant, that is the part of the quadratic formula under the radical. If you come up with something other than an perfect square, then the quadratic does not have rational factors, i.e. it is time to move on to another technique.
Completing the square is valuable in two situations: First, when you are learning the concept in preparation for development of the quadratic formula, and second when you want to transform a general second-degree equation in standard form into vertex form so that you can identify and graph the conic.
All other situations call for the quadratic formula. If you forget the quadratic formula, you can always take the time to complete the square on to derive it -- but memorizing the formula is MUCH easier.
