Is it just me or has "factorise" (with s or z) suddenly become much more common term for "to factor" recently?
Before I went to America, I had never seen factor used as a verb, at least in a mathematical context: you don't ration a denominator, so why would you factor a polynomial?
This isn't the place for a British1 English vs American English argument, though, so I'll just leave this sack of 'U's for them to put back into words whenever they want, point out that football is a game in which a ball-shaped object is propelled mainly by the feet, resolutely put an 's' on the end of maths and carry on with my post.
So, yes, the usage (as far as I can see) is split pretty much by the Atlantic Ocean - digging out an O-level paper from 1940 (which, I think, Murray Walker might have sat!), 'factorise' is the verb of choice; I've not been able to find a similar reference for 'factor' in the US, because I'm short of time, but I'd be interested to hear of one.
@onthisdayinmath[s] points out that looking at the Google Ngram, the use 'factor' as a verb is much higher in the British English corpus than 'factorise' -- which is a surprise, until you realise two things: many American books appear when you click on 'factor' in the box below the graph, and 'factor' is used as a verb outside of maths.
The second point can be mitigated by searching for 'factor[ise/ize] the expression', which gives a much more even graph -- factor is still the winner in the British English corpus (although factorise is steaming up through the 90s and may well have overtaken.) Factorize was popular in the late 1950s, perhaps as the '-ize' usage was more common then.
By comparison, searching the American English corpus, 'factor the expression' is the only one to show up.
In summary, I don't think 'factorise' is getting more popular in American English - it seems much more likely that @onthisdayinmath[s] is simply reading more material from the UK.