1. Have each student in the class make up 10 trinomials (in one variable)
with integer coefficients between -10 and 10. Encourage variety--some
trinomials should have coefficients close to the extreme values, some
closer to 0 and some where the coefficients are all positive, all negative,
vary from one extreme to the other, etc.
2. Have each student use their SAS to factor the trinomials over the
rational numbers and record how many are factorable over the rational
numbers.
3. For all of the trinomials the class made up, find the ratio of
factorable trinomials to non-factorable trinomials and discuss the
probability that a trinomial that is randomly generated is factorable. How
does the question change if the coefficients come from a wider range of
integers, -100 to 100, for example? are not necesarily integers?
For a variation, discuss factorability over the real numbers and compare
factorability to roots and graphs of the parabola. In this way, we push
the envelope of the pure math concepts possible in Intro to Algebra and
begin to train students to "think mathematically", not just do symbolic
manipulations.
Martha
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