Using the Factor Theorem, it is found that yes, it is possible for a sixth degree polynomial function with integer coefficients to have no real zeroes, as they can have three complex-conjugate pairs.
<h3>What is the Factor Theorem?</h3>
The Factor Theorem states that a polynomial function with roots is given by:
In which a is the leading coefficient.
If a complex number is a root of a function, it's conjugate will also be a root. Thus, with three pairs of complex-conjugate roots, for example, , a sixth degree function with no real zeros is formed, so the answer is Yes.
More can be learned about the Factor Theorem at brainly.com/question/24380382