Expert: Paul Klarreich - 3/3/2008

Question
What makes certain quadratic equations unfactorable?

Answer
Questioner:   Heather
Category:  Advanced Math
Private:  No
 
Subject:  quadratic equations
Question:  What makes certain quadratic equations unfactorable?
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Hi, Heather,

Better you should ask:

What makes certain quadratic equations factorable?

In actuality, practically EVERY one is unfactorable.  But the math teachers -- those slimy bastards -- have managed to find the few that can be factored and filled the math books with them, so you sweet, innocent students get the idea that the unfactorable ones are the exception.

HOWEVER, I think you meant to ask this question:

Is there a way to tell that an equation is unfactorable BEFORE I go crazy trying to factor it?

Yes, Heather, there is a Santa Claus -- I mean, there is a method.  You have learned the Quadratic Formula, I assume.  It contains a piece, called the DISCRIMINANT, which I will call D, and which is:

D = b^2 - 4ac.

Compute it for your equation.  If it comes out to a perfect square (and positive, too) then the equation can be factored.  [Zero counts as a perfect square, too.]

That's all there is.