Question 11
Let $f_0$, $f_1$, $f_2$ and $f_3$ be polynomials in $\mathbb{R}[X]$ such that $f_k(1) = f_{k+1}(0)$, $k = 0, 1, 2, 3$ (indices are reduced modulo $4$). Show that there exists a polynomial $f$ in $\mathbb{R}[X, Y]$ such that $f(X, 0) = f_0(X)$, $f(1, Y) = f_1(Y)$, $f(1 - X, 1) = f_2(X)$, and $f(0, 1 - Y) = f_3(Y)$.