Fundamental Theorem of Algebra
This is a very powerful algebraic tool.2.4 It says that given any polynomial![]()
![\begin{eqnarray*}
p(x) &=& a_n x^n + a_{n-1} x^{n-1} + a_{n-2} x^{n-2} + \cdots
+ a_2 x^2 + a_1 x + a_0 \\
&\isdef & \sum_{i=0}^n a_i x^i
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/mdft/img157.png)
we can always rewrite it as
![\begin{eqnarray*}
p(x) &=& a_n (x - z_n) (x - z_{n-1}) (x - z_{n-2}) \cdots (x - z_2) (x - z_1) \\
&\isdef & a_n \prod_{i=1}^n (x-z_i)
\end{eqnarray*}](http://www.dsprelated.com/josimages_new/mdft/img158.png)
where the points are the polynomial roots, and they may be real or
complex.
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