# How can I show these polynomials are not coprime? x,\ x-1

How can I show these polynomials are not co'?
and $x+1$ in the ring ${\mathbb{Z}}_{6}\left[x\right]$
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Step 1
The ideal equals the ideal
and this is not the whole ring, otherwise
, so $1=2f\left(x\right)+\left(x-1\right)g\left(x\right)$.
Now send x to 1 and get a contradiction.