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I feel like there's not really an "easy" way to find out whether a compound is a polydentate, but I think the best way is to write out the Lewis diagram and see whether there are multiple locations where the ligand can bond with the metal cation. Also take into account the sigma and pi bonds (single/double/triple) to see whether those bonds can actually rotate or not.
I think the only way would be to draw the Lewis structure and see if it is attached to the central atom by 2 or more bonds. Knowing the number of donor atoms with electron pairs can also help identify if it would be a polydentate.
There's no easy way to know whether a coordination compound is polydentate, for this it is helpful to draw the lewis structure. But it is also good to know that bidentate ligands are ethylenediamine (en), and the oxalate ion (ox). Ethylenediaminetetraaceticacid acid (EDTA) is a hexadentate ligand and diethylenentriamine(dien) is a tridentate.
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