How do you find the factors of quadratic expressions? - Answers

Suppose you have the expression x2 + 7x + 12. You look for two numbers that add to 7 and multiply to make 12. They are 3 and 4. You put these numbers into the factors as follows: (x+3)(x+4). <> Here is a harder example. x2 - 5x - 36. The numbers have to multiply to make -36, so one must be negative and the other positive. Since they add to -5, the big number must be negative. If you're stuck, make a list of the pairs of factors of 36: 1x36, 2x18, 3x12, 4x9, 6x6. The numbers we are looking for are 4 and -9, and the factors are (x+4)(x-9). <> These two examples are 'easy' trinomials, since they have no number in front of the x2. 'Hard' trinomials do have a number there. For example, 3x2 - 19x -14. There are several ways of doing this, but it is basically organized trial and error. The factors are (3x+2)(x-7).