understanding the factorisation machine formula

I am reading this tutorial about factorisation machines.

I get the intuition behind it, compute the dot product between the (user/item)+(item/aux features)+(user/aux features). This dot product can impact y_hat.

But I don't understand the formula below. I understand the first section, the bias. I understand the second section, first order weighting.

But I don't understand the last section.

I understand the v,v, this could be dot product of user,item or item, aux feature. But what are the x's? Would these be scalar values?

Also can someone just confirm that $P$ would be 3 in my example as that is users, items and aux features.