Let F3 0 1 2 be the field with three elements Let fx x2 be

Let F₃ = {0, 1, 2} be the field with three elements. Let f(x) = x² be a polynomial in F₃[x].  What is the residue of least degree of f(x) modulo x² + x + 2.

x + 1

x + 2

x

2x + 1

Solution

the residue of least degree is x+2 since

their difference is divisible by x^+x+2.