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Topic: defense of factoring (was:equation with inverse trig fcn???HELP)
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 Joshua Zucker Posts: 710 Registered: 12/4/04
defense of factoring (was:equation with inverse trig fcn???HELP)
Posted: Apr 13, 1998 5:19 PM
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My defense of factoring is that I want students to learn that:
1) there is a connection between the factors and roots of a polynomial
2) there is a connection between the coefficients and roots of a polynomial.

I think practice with factoring and multiplying simple polynomials is
one good way to lead students to that understanding.
Of course there are other ways, maybe better ways, to emphasize these
ideas. And for some students, the simple arithmetic of factoring
becomes a memorized algorithm and they lose sight of these two ideas.

One thing I have particularly noticed is that factoring by grouping
helps students get the idea that they can treat larger chunks, like
2x+1, just the same way as they would a variable like y.

Hey, I can make this relevant to ap-calc now! That idea, first
learned in beginning algebra I hope, is crucial to understanding the
chain rule (and its inverse, u-substitution for integration). So I
hope we keep teaching factoring by grouping! If not, we need to
replace it with some other situation that makes the students see this
idea of chunking.

--Joshua Zucker

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