I am looking for the primary decomposition of $(x^2,xy,xz)$ in $k[x,y,z]$ where $k$ is a field.
I am not looking for a solution here, rather a hint or two. Is there a general strategy for approaching primary decomposition? I realize that you have to make an educated guess first, but I am not sure where to start. Possibly a resource with a few worked out examples would help.