Question

Are all polynomial expressions factorable?

Answer 1

No; at least not if you are restricted to Real values.

Explanation:

As a simple example
`color(white)("XXX")x^2+2` is not factorable with Real values.
A polynomial expression will only be factorable if it crosses or touches the X-axis.

Note, however, if you can use Complex (so called "imaginary") numbers then all polynomials are factorable.