Number Theory and Algebra Summary
Wednesday, July 3, 2002
The topic today was simply (!) factoring... how do we choose coefficients for quadratic trinomials so that they would factor "nicely". We started, of course, with working backwards, choosing our factors and then expanding and simplifying. This, though, was not sufficient for us so we delved further.
We found patterns relating to ax^2 + bx + ___ to determine possible values for c and likewise ax^2 + ___x + c to determine possible values for c. We then went further and introduced the Factor Theorem to develop a formal rule for finding all possible families of quadratic trinomials that would work "nicely".
We ended the day by cautiously approaching cubic polynomials.
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This material is based upon work supported by the National Science Foundation under Grant No. 0314808.