when do you know you cannot factor a quadratic relation, and know when exactly to use quadratic formula??

Question

I know how to factor and how to use the quadratic formula... but however I can't seem to grasp, when to use quadratic formula. I mean when a relation cannot be factored, but how do you determine it cannot be factored?

Answer 1

Try evaluating the discriminant in the quadratic formula, which is

 

b² - 4ac

 

 

If the discriminant is a perfect square, then you can factor the equation using FOIL.  This is because when you put the discriminant into the quadratic formula, you will obtain two solutions that are rational rather than irrational.  Those integer solutions can be turned into linear factors that you would multiply together.

 

For example:

 

if   x=r   and   x=-k       are solutions, then the linear factors of the equation would be   (x - r) and (x + k) .

 

 

However, if the discriminant is NOT a perfect square, then go on to use the quadratic formula.

Answer 2

This is the process that I follow:

GCF - if present

General Forms - perfect square, difference of squares if present

FOIL - if possible

Formula