Factorization of Polynomials - Irreducibles - Anderson and Feil

[Math Amateur]

I am reading Anderson and Feil - A First Course in Abstract Algebra.

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

After this they challenge the reader with the following exercise:

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

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

Peter

 

[Sudharaka]

I am reading Anderson and Feil - A First Course in Abstract Algebra.

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

After this they challenge the reader with the following exercise:

Show that x^4 + 2 is irreducible in \mathbb{Q} [x]. taking your lead from the discussion of x^2 + 2 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.

 

[Math Amateur]

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.

Thanks - most helpful - appreciate your help

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

 

[Sudharaka]

Thanks - most helpful - appreciate your help

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

To if you want to delete your previous attachments go to "http://www.mathhelpboards.com/usercp.php" and then click on the "http://www.mathhelpboards.com/profile.php?do=editattachments" under the "My Settings" pane. Hope this will work for you. :)