Palindromic Polynomial - Factorization

Factorization

Factorization techniques (and the search for roots) follow on directly from the properties listed above.

For example Property 5 yields an immediate factor x+1 for palindromic polynomials of odd degree.

As another example Property 8 leads to the technique of dividing by xd and replacing x + 1/x by xX.

As an example of the latter technique suppose

Letting X = x + 1/x, dividing by x2 and deriving

we have the much simpler

which factorizes as

so either X = 1 or X = - 1

The X = - 1 case yields

or

which has no real roots.

The X = 1 case yields

or

which also has no real roots.