Question

f,g apartin Z3[x],unde f=x patrat +x , g=xpatrat +2x^+a,a apartinand de Z3. calculati f(0^) +f(1^)

Answer 1

$f,g \in \mathbb{Z}_3[x],\quad f = \hat{x}^2+\hat{x}\\ \\ f(\hat{0}) + f(\hat{1}) = (\hat{0}^2+\hat{0}) + (\hat{1}^2+\hat{1}) = \hat{0}+\hat{2} = \boxed{\hat{2}}$