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ax^2+bx +c can be factored using

-The Quadratic Formula

-Factoring

-Completing the Square

For the quadratic formula we use the following formula for finding roots of the equation

x=-b+- sqrt(b^2-4ac)/4a

In the factoring method we have to make two factors which on multiplication gives the trinomial.There is a method in this which involves trial and error.

in the method of completing of square we have to transform the trinomial into a perfect binomial square.certain trinomial can be used to find out roots of the equation.

Please let me know if you need any clarification. I'm always happy to answer your questions.