Answer: Aphids are soft-bodied insects so a soap and water mixture will coat their skins and effectively kill them. The problem is that aphids give birth to live young, which are capable of giving birth almost immediately. So, if you miss just one young aphid, you'll have and entirely new population in just a matter of days. You'll either have to treat your plants daily or use something with some residual effect. I use Safer's Insecticidal Soap, which is acceptable to organic growers. It has some residual effect, but I still use it 3 days in a row, carefully spraying the undersides of leaves and stems to make sure I get all the aphids and their offspring. This treatment usually lasts 4-5 weeks and then I have to do the 3 day treatment again, but at least I feel as though I'm in control. I don't think the banana peel will have any effect on the presence or absence of aphids, but it could attract fungus gnats which are an unpleasant critter to deal with.
Best wishes with your garden!
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