As an illustration, it should be pointed out that this theorem is equivalent to the statement that every polynomial

`C`_{n}x^{n} + C_{n-1}x^{n-1} + ... + C_{1}x + C_{0}

can be factored, that is put in a form

`(x-r`_{1}) * (x-r_{2}) * ... * (x-r_{n})

which, when expanded algebraically and simplified, will yield the original polynomial.

r_{1}, r_{2}, 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.