How can I easily know whether I can factor from before (even without doing it)? And is it possible to do it?

Question

phi · Answer

not easily.  The only "clue" is if it's on a test and the numbers are reasonably small, it probably is factorable.  In the real world, you would use a computer to figure things out.

anonymous · Answer

You can use the discriminant of a quadratic equation in order to determine if the equation is "prime." Equations that are not prime may be factored, whereas prime ones cannot be factored (and then you'll have to use the quadratic formula to solve for your variable(s).

Quadratic Equation:
$$ax^2 + by^2 + c $$

Discriminant:
$$b^2 - 4ac$$

If you get a negative discriminant value (discriminant < 0), the equation is prime and not factorable.

anonymous · Answer

To clarify, a negative discriminant means that you have no "real" roots, but imaginary roots are still possible.

anonymous · Answer

Sorry I meant $$ax^2 + bx^2 + c$$

calculusxy · Answer

i have the equation 
$-6p^2 - 17p - 56$ 

if i do use the discriminant, i would have $b^2 - 4ac = -17^2 - 4(-6)(-56)$ 
$289 - 1344$ 
it will be a negative, so it's prime.
right?

phi · Answer

a negative discriminant means the factors are complex (have an imaginary number in them).  That usually means no solution (though sometimes in physics, we can make sense of a complex number)

calculusxy · Answer

Thank you!