**OAF.FTA **

The Fundamental Theorem of Algebra (Polynomial Form):

For any polynomial function,$f$, of degree $n$, there exists
numbers $A$ and "roots", $r_1,r_2, ... , r_m$, "powers",
$p_1,p_2, ... , p_m$, and related linear functions, $f_j(x) =(x-
r_j)^{p_j}$, with $ j = 1,2, ... , m$, and a monic
polynomial $g_f$ which has no real roots, so that $f$ can be
expressed as a product :

**$f(x) = A*f_1(x)*f_2(x)*...*f_m(x)*g_f(x)$**

**Furthermore: If $g_f \ne 1$** then there are "vertices,"
$(h_1,k_1), (h_2,k_2) ... (h_s,k_s)$ with $k_i > 0$ for
all $i$ and powers $t_1,t_2, ... , t_s$, and related quadratic
functions $q_{i}(x)=((x-h_i)^2 +k_i))^{t_i}$ so that $g_f$
can be expressed as a product:

**:**

$ g_f(x)=q_1(x)*q_2(x)*...*q_s(x)$