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Which of the following are false?

We denote by $(P)$ the ideal generated by $P$ in the ring in question.

Select ALL that apply.

$({\mathbb Z}/3{\mathbb Z})[x]/(x^2+1)$ is a field

$({\mathbb Z}/5{\mathbb Z}[x])/(x^2+1)$ is a field

$(x^2+1)\subseteq (x-2)$ in $({\mathbb Z}/5{\mathbb Z})[x]$

$x^2+1$ is reducible in $({\mathbb Z}/15{\mathbb Z})[x]$

$(x^2+1)\subseteq (x+2)$ in $({\mathbb Z}/5{\mathbb Z})[x]$