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=== Factoring parallel polynomials ===
As with a [[polynomial]] under addition, a parallel polynomial with coefficients <math>a_k</math> in <math display=inline>\widetilde\C</math> (with {{nobr|<math>a_0 \neq \infty</math>)}} can be factored into a product of monomials:
:<math>\begin{align}
&a_0x^n \parallel a_1x^{n-1} \parallel \cdots \parallel a_n =a_0(x \parallel -r_1)(x \parallel -r_2)\cdots(x \parallel -r_n)
\end{align}</math>
for some roots <math>r_k</math> (possibly repeated) in <math display=inline>\widetilde\C.</math>
Analogous to polynomials under addition, the polynomial equation
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