Give all the ways of factoring $x^2$ into polynomials of degree 1 in $\mathbb{Z}_9[x]$; in $\mathbb{Z}_5[x]$.

Question

This question originates from Pinter's Abstract Algebra, Chapter 24 Exercise C7.

Give all the ways of factoring $x^2$ into polynomials of degree 1 in $\mathbb{Z}_9[x]$; in $\mathbb{Z}_5[x]$.

Attempt:

In $\mathbb{Z}_9[x]$, there are 2 ways:

$x^2\,\equiv (x)(x) \equiv(x+3)(x+6).$

In $\mathbb{Z}_5[x]$, there is only 1 way:

$x^2\, \equiv (x)(x)$.

Correct?