Write the quadratic in standard form: ax^2 + bx + c
Factor out any greatest common factor first
Find two numbers that multiply to ac and add to b
Rewrite the middle term using those two numbers
Group the terms into pairs
Factor each pair
Factor out the common binomial
Check by multiplying the factors back together
If a = 1, look for two numbers that multiply to c and add to b
If a ≠1, use the ac method or trial and error
If the quadratic is a perfect square trinomial, write it as a binomial squared
If the quadratic is a difference of squares, write it as two binomials
If it cannot be factored over integers, use the quadratic formula