You are teaching a basic algebra course and arrive at the section that deals with the factorization of quadratic trinomials. The textbook devotes fifteen pages to this topic, which it treats by trial-and-error methods. It mentions reverse FOIL, factoring by grouping, and the ac-method. Even after all this hassle, students are only expected to be able to factor trinomials no harder than, say, 12x2 − 31x − 30. The trinomial 120x2 − 371x + 98 probably does not appear as an exercise; 323x2 + 2986x − 8029 certainly does not
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