Solution
= Solution
In <characteristic two>, the <binomial theorem> gives $X^8-1=(X-1)^8$. The only root is already in $\mathbb F_2$, so the <splitting field> is the original <field>, despite the repeated root:
$$
\boxed{[K:\mathbb F_2]=1.}
$$
= Solution
In <characteristic two>, the <binomial theorem> gives $X^8-1=(X-1)^8$. The only root is already in $\mathbb F_2$, so the <splitting field> is the original <field>, despite the repeated root:
$$
\boxed{[K:\mathbb F_2]=1.}
$$