Four decades ago, the professor who taught me P vs NP absolutely stuffed his explanation of the polynomial refactoring example, drawing sum of products on the board as his example - bugged the crap out of me because I could visualize code for an algorithm to refactor sum of products relatively easily - certainly in polynomial time. I brought that to him after the next lecture and he clarified: product of sums is the hard problem, well, yeah, obviously when you look at that nightmare. I assume he had been teaching it for about a decade as well, he certainly had been in the department that long and longer.