A quadratic trinomial is normally factored as the product of two binomials. Using the generic formula abx^2 + cx + d for the trinomial, its factors are (ax + y) and (bx + z) if y times z equals d and az + yb = c.
Continue ReadingConsider the trinomial 2x^2 + 9x - 5. The first term, 2x^2, can only be factored as the product of 2x and x. Therefore, the factors of 2x^2 + 9x - 5 are (2x + y) and (x + z) with y and z still to be determined.
Because the third term is negative, one of the factors must be negative, and the other must be positive. The only possible factors that can have a product of -5 are either 1 and -5 or -1 and 5.
There are four possible pairs of binomials: (2x + 5) and (x - 1), (2x - 5) and (x + 1), (2x + 1) and (x - 5), or (2x - 1) and (x + 5).The second term of the trinomial must equal the sum of, or difference between, the products of the outer and inner terms. Since 2x times 5 equals 10x and x times -1 equals -1x, the difference between these two products is 9x, so the only possible combination of binomials that can be the factors of 2x^2 + 9x - 5 are (2x - 1) and (x + 5).