A polynomial $$f(x)$$ is said to be reducible if it can be written as $$f(x) = g(x)h(x)$$ where $$\deg(g(x)) > 1$$ and $$\deg(h(x)) > 1$$. Otherwise it is said to be irreducible. If $$f(x)$$ is a polynomial of degree 2009, Choose the correct statement from the following.

A

There are infinitely many $$f(x)$$ that are irreducible

B

There are exactly 2009 $$f(x)$$ that are irreducible

C

$$f(x) = x^{2009} + 1$$ is an irreducible polynomial

D

There exists no $$f(x)$$ that is irreducible

E

none of these