Q&A #104

Teachers' Lounge Discussion: Factoring trinomials

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From: Elizabeth Appelbaum

To: Teacher2Teacher Public Discussion
Date: 2005012622:26:00
Subject: factoring trinomials

I read the interesting discussion on factoring trinomials. I suggest that factoring is overemphasized in the United States. The main reason for factoring is to solve equations. If the equation can be solved more easily with the quadratic formula, then that method should be used. In applied mathematics students encounter quadratic functions, most of which do not factor. Students should recognize easy factoring, like x^2 - 5x + 6 = (x -2)(x - 3), zeros 2 and 3. Most of the time they should use the quadratic formula. Students should be encouraged to factor over the reals and complex numbers ,rather than over the integers, so they learn the fundamental theorem of algebra: a polynomial of degree n > 0 with complex coefficients factors into n linear factors with complex coefficients. Equivalently, if the polynomial has real coefficients, it factors into linear and irreducible quadratic factors with real coefficients. The quadratic formula can be used to factor a trinomial. For example, the polynomial 6x^2 - x - 12 (Lloyd) has zeros 3/2 and -4/3, so it has linear factors (x - 3/2) and (x + 4/3). Since the leading coefficient is 6, the complete factorization is

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