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Topic: [math-learn] Re: Factoring in Algebra I
Replies: 2   Last Post: Feb 12, 2001 9:05 AM

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Posts: 10,730
Registered: 12/3/04
[math-learn] Re: Factoring in Algebra I
Posted: Jan 30, 2001 8:25 AM
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There are of course at least a dozen methods available to factor quadratic
trinomials (some specific -- like difference of perfect squares -- some
general, some devious -- like use the quadratic formula to find the roots and
work backwards -- some paper and pencil some electronic). That implies that
no one of them is that important.

What is important, IMHO or maybe just IMO, is that the student understand
that the factored and expanded form of a polynomial are both important and
useful; that each tell us different important and useful things about the
polynomial. But the procedure of going from the one to the other (especially
the expanded form to the factored form) is not important. It's a job for a
CAS. Okay, sure, have your students do a few simple ones to get a "feel" for
(not the procedure, but) the relationship between the two forms. Days of
instruction of "factoring" are largely a waste of time. The time would be
better spent in using the factored from to learn about the polynomial (graph,
roots, general shape, increasing, decreasing, etc.). I know that's a big step
for some. If you accept that a CAS can produce the factors, then you can
study, not just quadratic polynomials, but a much larger set of polynomials
and polynomials of higher degree. You can deal with polynomials that factor
over larger sets than just the integers (irrational, then complex numbers).

Another thing to consider is just how few quadratic polynomials actually
factor. For example if you limit the coefficients to relatively prime
integers between -20 and 20, only about 7% factor over the integers. The
percentage that factor is inversely proportional to the size of the
coefficients. As the coefficients increase in absolute value the percentage
that factor approaches zero.

Study polynomials, let the CAS do the factoring and expanding.


Lin McMullin
Niantic, CT.

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