JEE Math Practice Question

If $${a^2} + {b^2} + {c^2} = - 2$$ and f$$\left( x \right) = \left| {\begin{matrix} {1 + {a^2}x} & {\left( {1 + {b^2}} \right)x} & {\left( {1 + {c^2}} \right)x} \\ {\left( {1 + {a^2}} \right)x} & {1 + {b^2}x} & {\left( {1 + {c^2}} \right)x} \\ {\left( {1 + {a^2}} \right)x} & {\left( {1 + {b^2}} \right)x} & {1 + {c^2}x} \\ \end{matrix} } \right|,$$ then f$$(x)$$ is a polynomial of degree :

1. A.$$1$$
2. B.$$0$$
3. C.$$3$$
4. D.$$2$$