When you first start teaching math you quickly learn that some things that seemed simple or inconsequential to you are massive stumbling blocks for large numbers of students.
Factoring quadratics is one of these things.
Most people I encountered while majoring in math did not have a "method" to factor quadratics. You look at the thing, see if you can think of some factors, if you can't use the quadratic formula.
Students HATE this "process" it took me a long time to understand why. 1/
Consider:
x²+4x-60=0
"What do I do now?" Asks the student. And we tell them to write some parentheses like this:
(x ?)(x ?)=0
Hopefully the concept of multiplying binomials is a familiar one before you get to this. And the idea of the "zero product property" (I think the zero product property is so cool but have not found a way to get students as excited about it as I am... it's a pretty neat algebra trick... anyway)
When students see:
(x ?)(x ?)=0
They groan. 2/
@futurebird my first thought was: x＾2 +4x +4 - 64=0, then (x + 4)＾2 = 64, 64 = 8＾2. I can't see (x ?)(x ?) this time either.
@QED
That's the quadratic formula ... or rather it is the ancestor of the quadratic formula the process we call "completing the square."
But you can always write a quadratic as a product of binomials where the solution to each binomial solved as an independent equation is one of the roots.