Still trying to get a full understanding of primary decomposition, I had the ideal $$I=\langle x^3, x^2z^2, y^4, xy^3, x^2y^2\rangle$$
Using the method the user in this post I posted yesterday, I've got to a stage where I have $$(y^4,x) \cap (x^2,y^3) \cap (z^2,y^4,x) \cap (z^2,y^3,x^2) \cap (x^3,z^2,y^2)$$
I'm not sure where to go from here, what can I "remove" and whats the reasoning behind doing so?