Can someone please help me with the following question and explain to me what they are doing at each step:
In each case below, decide whether or not the given polynomial is irreducible over Q, justifying your answer in each case. If the polynomial is not irreducible , give its complete factorization into Q-irreducible factors.
i) (x^12) - 18(x^6) - 175
ii) (x^6) + (x^3) + 1
iii) (x^10) + 1