Is trisomy mostly due to complications with fertilization?
If so, does in vitro fertilization reduce the probability of trisomy for the fetuses of older mothers?
If not, can zygotes be screened before in vitro fertilization?
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Trisomy is due to non-disjunction in meiosis (the process in which eggs and sperm are created). This happens before fertilization.
Trisomies are more frequently seen in children of older women. It's not fully understood why this happens, but it is likely related to the fact that the oocytes do not complete meiosis (and become eggs) until ovulation. Here's an interesting paper that examines the physical causes of non-disjunction, but you might want to read up a bit more on meiosis (depending on your background) before tackling it.
You might screen for nondisjunction, but I don't think it's possible without killing the cells. See the Wikipedia page on karyotyping, which explains how an amniocentesis might be used for a prenatal genetic diagnosis. I don't know the regenerative capabilities of the human blastocyst, but if you had enough cells for a test, I don't think the blastocyst would develop normally.