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Reducible or irreducible

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Please see attachment ...

NOTE:
I need help for part iv) only

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Solution Summary

This shows how to determine if polynomials are reducible or irreducible.

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E = Q(root2, root3) and F = Q

(i) [E:F] = 4 and the basis is {1, root2, root3, root6}
You did this, and it is also an example in Fraleigh, fourth edition section 7.4

(iv) Start with (x + (root2 + root3))(x - (root2 + root3))

(playing with difference of squares which is often ...

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