# How do you know when to use factoring or quadratic formula?

Mar 30, 2015

This is actually a very good question, but not one with a really definitive answer. The following is mostly some rules of thumb.

If the quadratic looks particularly " ugly " use the quadratic formula. Quadratics with coefficients that involve roots would be one example of "ugly".

After that (if the "ugly" rule doesn't apply):
Factoring is usually faster and less prone to arithmetic mistakes (if you are working by hand).
If the coefficient of ${x}^{2}$ and the coefficient with no $x$ element have relatively few factors, time invested in attempting to factor the quadratic is usually worthwhile.
Also if you know the source of the quadratic, you can sometimes guess if factoring is likely to be successful (for example if it is a simple mathematical model of a situation or a question developed by a friendly math teacher).