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As part of my journey in understanding finite fields , I have a little problem with multiplying polynomials . Given: $(x^2+x-1)(x^2-x-1)$ , a normal multiplication would be :

$(x^2+x-1)(x^2-x-1)$ = $1 - 3 x^2 + x^4$

But this is incorrect since the correct answer (by the solution of my homework) is : $x^4 +x^2 +1$

Can you please clarify how to compute the modulo here ?

Regards

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    @ron: No. As as a *polynomial*, $x^6$ is just $x^6$; you don't do anything with the exponent. (Working over a finite ring/field, you have to be careful with the distinction between polynomials and polynomial functions, since different polynomials may define the same function). Powers of $x$ stay the same, you don't do anything with $x$ or with its exponents.2012-03-16

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