# Irreducible Polynomials

Not what you're looking for? Search our solutions OR ask your own Custom question.

Let f(x) = x^4 âˆ’ 8x^3 + 12x^2 âˆ’ 6x + 2. Show that f(x) is irreducible over

the field of rational numbers.

I know that it can't be factored... but how do I show its irreducible?

Â© BrainMass Inc. brainmass.com October 5, 2022, 6:26 pm ad1c9bdddfhttps://brainmass.com/math/basic-algebra/irreducible-polynomials-eisensteins-irreducibility-criterion-127340

#### Solution Preview

We can use the Eisenstein's Irreducibility Criterion.

Let p=2, then p is a prime. We ...

#### Solution Summary

Irreducible polynomials are investigated. The Eisenstein's irreducibility criterions are examined.

$2.49