How to factor polynomials with complex coefficients Factor completely the polynomials $$p(x)=5ix^4-(9+2i)x^3+7x+6-i$$ and $$q(x)=9x^5-x^3+7x+6$$ First, I tried to use the Fundamental Theorem of Algebra but it did no...--prophetes.ai

How to factor polynomials with complex coefficients Factor completely the polynomials $$p(x)=5ix^4-(9+2i)x^3+7x+6-i$$ and $$q(x)=9x^5-x^3+7x+6$$ First, I tried to use the Fundamental Theorem of Algebra but it did not work out. ThenI tried plugging in values like $x=-i,i-1$ and nothing worked. Can I have some hints on how to proceed?

Both polynomials are irreducible not merely over **Q** , but over $\mathbb Q[i]$ as well. Furthermore, the roots of the latter are inexpressible in radicals, and those of the former involve hideous expressions.