Question

What is meant by an irreducible quadratic denominator?

Answer 1

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^2-4ac` and check if it is negative.

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