Modulo Polynomial Division/Examples

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Examples of Modulo Polynomial Division

Arbitrary Example $1$

Let:

\(\ds \map f x\) \(=\) \(\ds x^3 - x^2 - 1\)
\(\ds \map g x\) \(=\) \(\ds x + 1\)


Then $\map f x$ divided by $\map g x$ modulo $3$ is:

$x^2 + x - 1$


Arbitrary Example $2$

Let:

\(\ds \map f x\) \(=\) \(\ds x^3 - x^2 - 1\)
\(\ds \map g x\) \(=\) \(\ds x + 1\)


Then $\map f x$ not divisible by $\map g x$ modulo $11$.


Arbitrary Example $3$

Let:

\(\ds \map f x\) \(=\) \(\ds x^3 - x^2 - 1\)
\(\ds \map g x\) \(=\) \(\ds x - 5\)


Then $\map f x$ divided by $\map g x$ modulo $11$ is:

$x^2 + 4 x - 2$
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