Hi My first post here,

I am very much confused, have wasted more than 7/8 hours on this single problem. But now I give up, can somebody please help me solve this. I do not yet know the correct answer to it, but what I am getting does not look right. Anyways, here is the problem:

Write down an analogue of the extended Eucliena Algorithm for the ring F2^[x]. Given that p(x) = x^8 + x^4 + x^3 + x + 1 is a (primitive) irreducible polynomial. Find the inverse of x^7 + x + 1 in the field

F2^8 = F2^[x]/(p(x)).

I have tried implementing the GCD way of factoring p(x) with (x^7+x+1) to get to a commond divisor, but that common divisor looks too huge to bt eright, this is what I am getting at the moment:

1-((-32x^2/5)+(208x/25)-(632/125))

Please suggest...