Suppose you have a λφ4 theory. Books only seem to calculate counter-terms for 2-pt and 4-pt functions. But what about 3 particles scattering into 3 particles? Do the counter-terms determined by renormalizing the 2-pt and 4-pt functions cancel divergences in 3x3 scattering? For example, take the graph below: Is it obvious that the counter-terms from 2x2 and scattering, along with counter-terms from the 2-pt function, can cancel this graph?