Bleach is generally not recommended for polyester fabrics; it doesn't react well with the fibers to remove color, and it can actually degrade the fabric. Nevertheless, the Clorox company prescribes a method for bleaching white polyester with chlorine bleach, and you can always substitute oxygen bleach as an alternative. Check the care label first -- if it specifies "No Bleach," proceed at your own peril. Instead of a sparkling white garment, you may end up with a dingy yellow one.
Bleaching With Chlorine Bleach
Soak severely soiled garments in a solution consisting of 1/4 cup of bleach per gallon of water. Immerse each item completely and allow it to remain for five minutes.
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Treat localized stains with a bleach gel pen. Never apply full-strength bleach directly to the garment -- or anything else.
Wash the garment in the hottest water recommended on the care label, adding 3/4 cup of regular bleach to the detergent.
Oxygen Bleach -- a Safer Alternative
Oxygen bleach is sodium percarbonate -- it's a mixture of sodium bicarbonate -- or baking soda -- and hydrogen peroxide. Like sodium hypochlorite, which is the active ingredient in chlorine bleach, sodium percarbonate reacts with the chromophores in the fabric, which are the molecules that reflect light and provide color, but sodium percarbonate is safer for fabrics. It may or may not remove the stains from polyester, but it won't turn it yellow, either.
Mix the bleach -- which comes in powdered form -- with water in the proportion recommended on the container label. In most cases, a suitable proportion is 1/2 cup of powder per gallon of water. Increase this to 1 cup per gallon of water for severely stained fabric.
Soak the stained fabric for an hour. It the stains are still there, it's safe to leave the fabric overnight.
Wash the fabric in the washing machine, using a high-quality laundry detergent. Use the hottest water recommended on the label, and add a cup of oxygen bleach to the wash water for maximum brightening.
Borax is also a whitening and cleansing agent. Add 1/2 cup to the washer water in addition to or in lieu of oxygen bleach.