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Topic: Polynomial (not quite) division
Replies: 13   Last Post: Jan 16, 2014 11:07 AM

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William Elliot

Posts: 1,440
Registered: 1/8/12
Re: Polynomial (not quite) division
Posted: Jan 16, 2014 5:05 AM
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> Hi, could anyone please help me with the following:
> As an example I'll start with the identity:
>
> (1 + x^-2)(x^3 + 1) = x^3 + x + 1 + x^-2
>
> Now if I were to use the standard polynomial division algorithm (I
> appreciate that x^-2 + 1 is not a polynomial) to work out
>
> (x^3 + x + 1 + x^-2) / (x^3 + 1)


= (x^5 + x^3 + x^2 + 1)/(x^5 + x^2)
= 1 + (x^3 + 1)/(x^5 + x^2)
= 1 + (x^3 + 1)/(x^2 (x^3 + 1)) = 1 + x^-2




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