Step 1: Recall why an element shows more than one oxidation state.
An element shows many oxidation states when electrons from more than one type of orbital are close enough in energy that all of them can be removed with a similar amount of energy.
Step 2: Compare actinoids with lanthanoids on this point.
In lanthanoids, the $4f$ orbitals sit well below the $5d$ orbitals in energy, so mostly only the outer electrons take part in bonding and $+3$ dominates. In actinoids, the $5f$, $6d$ and $7s$ orbitals lie much closer together in energy.
Step 3: Connect this energy closeness to the observed behaviour.
Because electrons in $5f$, $6d$ and $7s$ can all be removed with comparable energy, actinoids can lose different numbers of electrons under different conditions, giving oxidation states from $+3$ up to as high as $+7$ in elements like neptunium and plutonium.
Step 4: Rule out the other reasons offered.
Radioactivity, large atomic number and large atomic mass are true facts about actinoids, but none of them by themselves explains why the oxidation states vary so much; the real reason is the closeness in orbital energies.
\[ \boxed{\text{Comparable energies of } 5f, 6d, 7s \text{ orbitals}} \]