One person asks, Why teach synthetic division? and I’ll see that question and raise you a “Why teach polynomial division?”
I really can’t think of a good reason why synthetic division is still in the Algebra 2/PreCalculus curriculum. When I was in high school (at my HS, I was in the last class not to use graphing calculators), synthetic division was a handy shortcut because we had to do tons (often enough for a whole page for one problem) of divisions to test potential zeros for higher-order polynomials. However, with technology as it is, I can think of better ways to spend the 2-3 days it would take to cover synthetic division and finding rational zeros by hand.
I do still teach polynomial division, because it is useful for finding polynomial asymptotes of “improper” rational functions. But for the synthetic division shortcut, unless I’m doing tons and tons of polynomial division problems (and only the case where we’re dividing by linear factors at that), I really can’t think of a good…
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