Represent a polynomial as a composition of polynomials:

Compositions of the same polynomials in different orders:

A decomposition with three polynomials:

A composition of more than two polynomials:

No decomposition:

A polynomial with symbolic coefficients:

A polynomial with complex coefficients:

Decompose a polynomial over the integers modulo 3:

Solve some polynomial equations of degrees higher than 4 in terms of radicals:

Solve by solving and then etc:

Check that these indeed are the roots of f:

Wolfram Language solvers use Decompose automatically:

Composition of polynomials given by Decompose gives the original polynomial:

Use Fold to compose the polynomials:

Use Expand to show that the result is equal to f:

Use Factor to represent a polynomial as a product of irreducible factors:

f can be factored but not decomposed; g can be decomposed but not factored:

Decompose ignores possible decompositions with inner polynomials that are linear: