Hi Sandy,
That's sort of like asking where the fact that 3 + 5 = 8 is used in
accounting. The point is that it comes up, and it comes up often.
The factoring of trinomials is not a topic in physics courses, but the
mathematics used to analyze physical situations often involves the
factoring of trinomials. If you really need examples, then you will have to
wait a while, since I would have to look at all my old physics books.
However, I taught physics for seven years at various colleges, and
factoring was just one of the many mathematical tools that were used to
analyze physical situations. It did not occur rarely.
And one of the places where such factoring does come up is in some problems
analyzing the motion of an object in a constant gravitational field. Why do
you talk about such polynomials as being "difficult to contrive?" They are
just as easy as any other thing to contrive. Perhaps you are bothered by
the "contrived" examples in physics textbooks? Well, I guess I don't think
of them as being as contrived as you do, nor do I think of "contrived" as
being as negative an adjective as you seem to consider it. When developing
a physics problem, you want the emphasis to be on the physics, not the
math, so you necessarily make up examples with numbers (such as 32 ft/sec^2
for the acceleration due to gravity; it's not *exactly* 32) that make the
math work out nicely. I don't think of that as contrived, at least not in
the pejorative sense which you seem to intend.
If your students do not learn to factor trinomials, they will be at a
disadvantage in physics courses. Anyway, factoring trinomials with leading
coefficient equal to 1 is hardly rocket science, and if the leading
coefficient is not equal to 1, they can always use the quadratic formula,
or one of the other three (that I know of) ways of factoring such a
polynomial.
mark snyder
fitchburg state college
msnyder@fsc.edu,msnyder@tiac.net
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