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## Homework Statement

Find the degree of the splitting field of the following:

[tex]x^6+x^3+1[/tex]

## Homework Equations

## The Attempt at a Solution

Can I do this?

Let [tex]y=x^3[/tex]

then

[tex]y^2+y+1[/tex]

has degree 2 over Q (From another problem)

So the degree of the splitting field is 2.

Or do I need to factor it out?

or do I need to look at the roots of the origional polynomial?

The method here is what I am confused about.

Thanks

CC

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