Question concerning decomposition

Hello

two questions:

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a) Write as a direct sum.

b) Why doesn't exist a direct sum decomposition of ?

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a) Since the roots of f are contained in the field considered. y is a root of f if it's a root of h or it is a root of g. So my decomposition here is

Is it correct and what about my reason? 9=3^2 but why can that not be decomposed more?

b)

Are the numbers choosed with this factorisation for causing confusion only? My reason here is:

If y is a root of it is not a root of a polynomial dividing f(y) of a lower degree. No matter what is the ys contained in the field considered at b) are only 0 when powered to 160675.

What do you think of my explanations? How would you reason here?

Regards