  The Fibonacci polynomials are defined recursively as
$f_{n}(x)=xf_{n-1}(x)+f_{n-2}(x)$, where $f_0(x) = 0$ and $f_1(x)= 1$. We
generalize these polynomials to an arbitrary number of variables with the
$r$-Fibonacci polynomial. We extend several well-known results such as the
explicit Binet formula and a Cassini-like identity, and use these to prove that
the $r$-Fibonacci polynomials are irreducible over $\mathbb{C}$ for $n \geq r
\geq 3$. Additionally, we derive an explicit sum formula and a generalized
generating function. Using these results, we establish connections to ordinary
Bell polynomials, exponential Bell polynomials, Fubini numbers, and integer and
set partitions.
