Answer
angular acceleration is increasing with time so it is not constant
Work Step by Step
Angular velocity of object is:
$w=\dfrac {\partial \theta }{\partial t}=\dfrac {\partial }{\partial t}\left( 2+4t^{2}+2t^{3}\right) =8t+6t^{2}.....\left( 1\right) $
Angular acceleration of the object is:
$\alpha =\dfrac {\partial w\left( t\right) }{\partial t}\left( 2\right) $
Using (1) and (2), we get
$\alpha =\dfrac {\partial w\left( t\right) }{\partial t}=\dfrac {\partial \left( 8t+6t^{2}\right) }{\partial t}=8+12t......................(3)$
As we can see from the equation (3), the angular acceleration is increasing with time so it is not constant.
