If $a^2+b^2+c^2=-2$ and $f(x)=\small\begin{vmatrix}1+a^2x&(1+b^2)x&(1+c^2)x\\(1+a^2)x&1+b^2x&(1+c^2)x\\(1+a^2)x&(1+b^2)x&1+c^2x\end{vmatrix}$ then $f(x)$ is a polynomial of degree

Question

$(a)\;1\qquad(b)\;0\qquad(c)\;3\qquad(d)\;2$