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\begin{abstract}
The Fibonacci sequence's initial terms are $F_{0}=0$ and $F_{1}=1$,
with $F_{n}=F_{n-1}+F_{n-2}$ for $n \geq 2$. We define the polynomial
sequence ${\bf p}$ by setting $p_{0}(x)=1$ and
$p_{n}(x)=xp_{n-1}(x)+F_{n+1}$ for $n \geq 1$, with
$p_{n}(x)=\sum_{k=0}^{n}F_{k+1}x^{n-k}$. We call $p_{n}(x)$ the {\it
Fibonacci-coefficient polynomial (FCP) of order $n$\/}. The FCP
sequence is distinct from the well-known Fibonacci polynomial sequence.
\par We answer several questions regarding these polynomials.
Specifically, we show that each even-degree FCP has no real zeros,
while each odd-degree FCP has a unique, and (for degree at least $3$)
irrational, real zero. Further, we show that this sequence of unique
real zeros converges monotonically to the negative of the golden ratio.
Using Rouch\'e's theorem, we prove that the zeros of the
FCP's approach the golden ratio in modulus.  We also prove a general
result that gives the Mahler measures of an infinite subsequence of the
FCP sequence whose coefficients are reduced modulo an integer $m\geq
2$.  We then apply this to the case that $m=L_n$, the $n^{th}$ Lucas
number, showing that the Mahler measure of the subsequence is
$\phi^{n-1}$, where $\phi=\frac{1+\sqrt{5}}{2}$.
\end{abstract}

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