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 ?