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I understand the idea of modulo with integers but I am having an incredibly hard time wrapping my head around the idea of modulus with polynomials. I am taking a course in which I need to divide polynomials in terms of a specific modulus. I am able to divide the polynomials but don't understand how the mod applies.

So for example, $f(x)$=$$4x^4+2x^3+6x^2+4x+5$$ and $g(x)$=$$3x^2+2$$ and I am asked to divide f(x) by g(x) in mod 7.

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All you need is computing the inverse of the leading coefficient modulo $7$. The operations are the same as in $\mathbf R$, but you compute modulo $7$. Here is an example:

enter image description here

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  • $\begingroup$ When multiplying by 3x, how did you get $2x^3-x^2$? Wouldn't it be $2x^3-x$ because there is no x in the denominator? $\endgroup$ – 123choq456 Oct 26 '15 at 2:20
  • $\begingroup$ I think you're right. I'll modify my answer in a moment. $\endgroup$ – Bernard Oct 26 '15 at 2:31

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