A carbon tax could work. Cap & trade could work. Carbon capture could work.
"Could" is the key word there.
You have to be careful how you implement these programs, as the law of unintended consequences rears its ugly head.
Case in point, current independent carbon offset programs have largely been shown to be abject failures at actually reducing total carbon consumption. These are programs of the sort where a company buys credits in some charitable activity meant to reduce carbon production in another part of the world, in order to offset their own production which would be much more difficult or expensive to reduce.
The classic example of this is a charity that sold carbon credits to fund higher efficiency stoves in a region where 3-stone fires are still used. For reference, a 3-stone fire is literally 3 equal sized stones with a fire between them and a pot on top of the stones to cook meals, like you'd make if you were camping. This is basically the least efficient type of fire possible, with something like 70-80% of the heat going into the open air rather than the pot. This requires a huge pile of wood to burn daily just to meet the cooking needs of a small family.
So the charity comes in and introduces these cheap but efficient stoves that put more like 50-60% of the heat into the pot rather than 20-30%. The idea is obviously with the higher efficiency stove the family will need to burn far less wood. This reduces carbon emissions overall, and frees up some time spent gathering wood that can be put to more productive activities. Sounds like a great strategy right?
But that's not what actually happens! No, what happens is the family doesn't reduce their wood consumption at all! They KEEP the 3-stone fire and run it along side the high-efficiency stove! Their daily output trebles, only now their producing enough cooked goods that they can sell some on the side, or they can better support extended family members who may have been struggling, etc. Great for that family and community that is receiving these stoves en-masse, no doubt, but little to no carbon reduction!
These credits end up being sold as worth say 10lbs of carbon offset each, when the reality is that they are worth maybe 0.5lbs of carbon offset each, if that.
This has happened to pretty much all of these carbon offset charities, because they totally fail to accurately predict human behavior.