# Factorization of Polynomials - Irreducibles - Anderson and Feil

#### Peter

##### Well-known member
MHB Site Helper
I am reading Anderson and Feil - A First Course in Abstract Algebra.

On page 56 (see attached) ANderson and Feil show that the polynomial [TEX] f = x^2 + 2 [/TEX] is irreducible in [TEX] \mathbb{Q} [x][/TEX]

After this they challenge the reader with the following exercise:

Show that [TEX] x^4 + 2 [/TEX] is irreducible in [TEX] \mathbb{Q} [x][/TEX]. taking your lead from the discussion of [TEX] x^2 + 2 [/TEX] above. (see attached)

Can anyone help me to show this in the manner requested. Would appreciate the help.

Peter

#### Sudharaka

##### Well-known member
MHB Math Helper
I am reading Anderson and Feil - A First Course in Abstract Algebra.

On page 56 (see attached) ANderson and Feil show that the polynomial [TEX] f = x^2 + 2 [/TEX] is irreducible in [TEX] \mathbb{Q} [x][/TEX]

After this they challenge the reader with the following exercise:

Show that [TEX] x^4 + 2 [/TEX] is irreducible in [TEX] \mathbb{Q} [x][/TEX]. taking your lead from the discussion of [TEX] x^2 + 2 [/TEX] above. (see attached)

Can anyone help me to show this in the manner requested. Would appreciate the help.

Peter
Hi Peter,

I don't see any attachments in your post. You can use a image hosting website such as TinyPic to upload images and link them here, if you have trouble attaching files.

To show that $$x^4 + 2$$ is irreducible over $$\mathbb{Q}[x]$$ you can use Eisenstein's Irreducibility Criterion.

#### Peter

##### Well-known member
MHB Site Helper
Hi Peter,

I don't see any attachments in your post. You can use a image hosting website such as TinyPic to upload images and link them here, if you have trouble attaching files.

To show that $$x^4 + 2$$ is irreducible over $$\mathbb{Q}[x]$$ you can use Eisenstein's Irreducibility Criterion.

The reason I did not upload the attachement was that I could not delete my old attachements - about 5 or so are there and they exceed my allowed quota _ I cannot seem to delete them

Peter

MHB Math Helper