/sci/ - Science & Math

>>11934373
Here's the question.
I was thinking that it would be [math]F=\{0,1,2,x,x+1,x+2,2x,2x+1,2x+2\}[/math], since any field with order 9 will have characteristic 3 and it's obvious that that field does have characteristic 3. I'm just confused as to what's meant by the first part regarding [math]x^2+1[/math] because wouldn't [math]F=\mathbb{Z}_3 / \langle x^2+1 \rangle[/math] be the same thing?