Answer: Your plant could be infested with whiteflies (if they fly away when you touch the leaf) or mealybugs (if they don't move). Or it could be aphids. Spraying weekly with insecticidal soap will deter all of these pests. You should be able to purchase insecticidal soap at your local garden center. You can also try spraying with a soapy water mixture. If the insects appear to be mealybugs--white, cottony-looking creatures that congregate in the area where the leaf meets the stem--try dabbing them with rubbing alcohol. Keep a very close eye on your other houseplants, as all these pests spread easily. At the first sign of the insects, begin spraying.
If there are multiple stems on your plant and they are thin, I suspect you have dracaena rather than a true palm. If there's a single, thick trunk, then you probably have a palm. Both do well in low to bright light and dry soil.
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