No closed form solution means you cannot write a program that will, given an arbitrary polynomial, tell you the solution. Which is what was claimed above. Obviously the solution exists, but there is no single algorithm that can tell you what it is.
When the solution is irrational, as is common for polynomials, it might be difficult to guess what it is based on knowing an approximation of it.
When the problem posed is "factor this polynomial", it's unheard of. This is the conceptual difference between "needing a number to work with" and "studying math".