  A second order polynomial sequence is of Fibonacci-type $\mathcal{F}_{n}$
(Lucas-type $\mathcal{L}_{n}$) if its Binet formula has a structure similar to
that for Fibonacci (Lucas) numbers. Under certain conditions these polynomials
are irreducible if and only if $n$ is a prime number. For example, the
Fibonacci polynomials, Pell polynomials, Fermat polynomials, Lucas polynomials,
Pell-Lucas polynomials, Fermat-Lucas polynomials are irreducible when $n$ is a
prime number; and Chebyshev polynomials (second kind), Morgan-Voyce polynomials
(Fibonacci type), and Vieta polynomials are reducible when $n$ is a prime
number.
  In this paper we give some theorems to determine whether the Fibonacci type
polynomials and Lucas type polynomials are irreducible when $n$ is prime.
