Answer: First off, you need to have a firm identification of the pest. There are some palms that naturally have spots along their stems (petioles) that look quite like mealy bugs. Measly bugs look like little dabs of white cottony fluff and will hop. Scale looks like flattened discs, usually dark colored, attached to stems or leaves.
In checking labels on different brands of pepper wax spray, I have not seen mealy bug specifically listed as one of the insects that it can control or repel, although scale is listed on some brands. More typically it is indicated for control of soft bodied insects such as aphids, mites, whiteflies and so on.
With mealy bugs, first wash the plant, either using a damp cloth or by setting in the shower or laundry sink and spraying with a gentle stream of tepid water. (Cover the soil with foil to protect it from splashing/overwatering.) Inspect frequently for re-occurrence as these tend to congregate in crevices and will continue to emerge.
Next is to follow up with hand picking, dabbing them with a cotton swab dipped in rubbing alcohol, or applications of commercially formulated insecticidal soap or horticultural oil.
Be sure to carefully read and follow the label instructions for application and follow-up sprays. In treating for these, take special care to inspect the crotches and joints, undersides of the foliage, and any crevices.
Scale unfortunately is far more difficult to control, although the same regime of handpicking, alcohol swabs and if the infestation is severe, soaps or oil should eventually be effective if you are diligent. Soaps are effective against the soft crawling stage while the oils should smother the hardened scales. Check your plant carefully under a bright light as they tend to reappear after treatment, they are quite difficult to stop. Again, be sure to read and carefully follow all of the label instructions.
BOth of these pests can spread to other plants, so you may want to isolate the palm.
You might also want to work with your county extension to obtain a specific identification of the pest and then based on knowing that, work out a control plan. Good luck with your palm!
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