i) $$f(x, y)$$ is the polynomial $$f_0(x)y^{2007} + f_1(x)y^{2006} + f_2(x)y^{2005} + \cdots + f_{2006}(x)y + f_{2007}(x)$$, where each $$f_i(x)$$ is a polynomial in $$x$$ with real coefficients, and ii) $$(x - \alpha)$$ is a factor of $$f(x, y)$$, where $$\alpha$$ is a real number. Then

A

there exists a $$f(x, y)$$ such that $$f_i(x) = x^2 + 1$$ for some $$i \in \{0, 1, 2, \ldots, 2007\}$$

B

there exists a $$f(x, y)$$ such that $$f_i(x) = x - \alpha + 1$$ for some $$i \in \{0, 1, 2, \ldots, 2007\}$$

C

there exists a $$f(x, y)$$ such that $$f_i(x) = (x - \alpha)^{2006} + 1$$ for some $$i \in \{0, 1, 2, \ldots, 2007\}$$

D

there exists a $$f(x, y)$$ such that $$f_0(x) = x^2 - (2\alpha + 1)x + (\alpha^2 + \alpha)$$

E

none of these