In this series, I’m compiling some of the quips and one-liners that I’ll use with my students to hopefully make my lessons more memorable for them.
Today’s one-liner is one that I’ll use when I want to discourage students from using a logically correct and laboriously cumbersome method. For example:
Find a polynomial and a constant so that .
Hypothetically, this can be done by long division:
However, this takes a lot of time and space, and there are ample opportunities to make a careless mistake along the way (particularly when subtracting negative numbers). Since there’s an alternative method that could be used (we’re dividing by something of the form or , I’ll tell my students:
Yes, you could use long division. You could also stick thumbtacks in your eyes; I don’t recommend it.
Instead, when possible, I guide students toward the quicker method of synthetic division:
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