Let $K$ be a knot with 3-genus $g$ and Alexander polynomial $\Delta_K(t)$. Define span of a polynomial in $t$ as difference between highest and lowest power of $t$, for example $$\operatorname{span} (9t^7 + 3t^6 - 8t^2) = 7-2 = 5.$$
My question is: when $\operatorname{span} \Delta_K = 2g$? (*)
According to https://web.northeastern.edu/beasley/MATH7375/Lecture18.pdf, this is true if $K$ is fibered, but there are knots which have $\operatorname{span} \Delta_K = 2g$ and are not fibered. For example $8_{11}$ is not fibered but satisfies the equality, with $g =2$ and $\Delta_K = 2-2t^4$. I hope that there exist some simple condition equivalent to (*) that doesn't involve genus.