# What is meant by an irreducible quadratic denominator?

Aug 21, 2014

Irreducible simply means that it can't be factored into real factors. So, an irreducible quadratic denominator means a quadratic that is in the denominator that can't be factored.

You can easily test a quadratic to check if it is irreducible. Simply compute the discriminant ${b}^{2} - 4 a c$ and check if it is negative.

$2 {x}^{2} + 3 x + 4$ is irreducible because the discriminant is $9 - 32 = - 23$
$3 {x}^{2} - 9 x + 5$ is not irreducible because the discriminant is $81 - 60 = 21$