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Generally atoms with polarizing power are the ones that cause large distortions in highly polarizable atoms ions. Atoms/ions that are able to do this are small cations since they want electrons and additionally due to their small size are able to hold on to their electrons more strongly. So when looking at the periodic table you will have recognize atomic/ionic radius and charge.
As the polarizing power of a cation increases with size, for the first 3 columns, as you move to right, their polarizing power decreases and as you move down, the polarizing power increases. But it's much better to be able to compare polarizing power from the size and charge than to figure out some sort of trend for this.
Polarizing power is usually associated with cations. The usual trend for this is similar to atomic radius in the sense that polarizing power increases as the size of the atom increases. Therefore, down a group the polarizing power increases and decreases as you go across a period.
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