Fundamental theorem of algebra (idea) by Gorgonzola

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

C_nxⁿ + C_n-1x^n-1 + ... + C₁x + C₀

can be factored, that is put in a form

(x-r₁) * (x-r₂) * ... * (x-r_n)

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.

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