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Polynomial Division

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For polynomials $ p$ and $ q$ with $ m=$degree$ \,q\le$degree$ \,p=n$ there exists two unique polynomials $ f$ and $ r$ with

$\displaystyle p = fq + r,$   degree$\displaystyle \,f = n-m,\,$   degree$\displaystyle \,r < m\,

This decomposition can be determined by division with remainder.

In particular for a root $ t$ of $ p$ follows that $ p(x) = f(x)(x-t)$ with degree$ \,f=n-1$ .


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  automatically generated 4/ 8/2008