As an illustration, it should be pointed out that this theorem is equivalent to the statement that every polynomial
Cnxn + Cn-1xn-1 + ... + C1x + C0
can be factored, that is put in a form
(x-r1) * (x-r2) * ... * (x-rn)
which, when expanded algebraically and simplified, will yield the original polynomial.
r1, r2, etc., are the roots of the polynomial. The theorem doesn't show how to factor the polynomial; indeed, there is no general algorithm for factoring polynomials, although Laguerre's Method comes close.