Polynomial Decomposition

A polynomial u(x) is called a composite polynomial if there are polynomials v(w) and w(x), both with degree greater than one, such that u is represented by the functional composition u(x) = v(w(x)). The composite expression v(w(x)) is also called a decomposition of u in terms of the components v(w) and w(x), and the process for finding v and w is called decomposing a polynomial. For example,

u{x) = x4-5x2 + 6 (5.1)

is a composite polynomial with decomposition given by

v(w) =w2 — bw + 6, w(x) = x2.