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Is x³ + 2x² + 3x + 1 reducible over Q? If not, why not? What...

Is x³ + 2x² + 3x + 1 reducible over Q? If not, why not?

What is an irreducible / primitive polynomial?

What does irreducible mean, what is a prime element? Can you give an example for a primitive that is not irreducible or vice versa?

What can you say about the ring R [x]?

Which qualities of rings do you know, can they somehow be ordered (main ideal ring, ZPE, Euclidean)? What do the associated polynomial rings look like?

How can I construct a body for a polynomial P over a field K, which decomposes P into linear factors?

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