Advanced Trinomials with Lead Coefficients

Students learn that a trinomial in the form ax^2 + bx + c (where c is negative), such as 5x^2 + 3x - 2, can be factored as the product of two binomials, in this case (5x - 2)(x + 1). The first term in each binomial comes from the factors of 5x^2, 5x and x. The second term in each binomial comes from the factors of the constant term, -2, such that the product of the outer terms plus the product of the inner terms equals the middle term, +3x. Note that if -2 and +1 are used as the second terms in the binomials (5x - 2)(x + 1), then the product of the outer terms, 5x, plus the product of the inner terms, -2x, is +3x, which equals the original middle term.