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.