Find a degree 6 polynomial with - 8 as a root, no other roots, and in which the coefficient of x^6 is 16. Assume that all (non-constant) factors of the polynomial correspond to real zeroes.

Answer 1

The question seems ambiguous. I suggest you repost with the exact original wording.

A polynomial of even degree cannot have one single real root. It is possible to have two coincident roots, but not just one.

It then goes on to say that
"Assume that all (non-constant) factors of the polynomial correspond to real zeroes."
So is the question asking for "a single root", or 6?