Let K denote a field. A polynomial f(x)∈K[x] is said to be
decomposable over K if f(x)=g(h(x)) for some
polynomials g(x) and h(x)∈K[x] with
1<deg(h)<deg(f).
Otherwise f(x) is called indecomposable. If
f(x)=g(xm) with m>1, then f(x) is said to be
trivially decomposable. In this paper, we show that xd+ax+b is
indecomposable and that if e denotes the largest proper divisor
of d, then xd+ad−e−1xd−e−1+⋯+a1x+a0 is either
indecomposable or trivially decomposable. We also show that if
gd(x,a) denotes the Dickson polynomial of degree d and
parameter a and gd(x,a)=f(h(x)), then
f(x)=gt(x−c,a) and h(x)=ge(x,a)+c.