In the previous article, I taught you how to multiply binomials into quadratic trinomials. Now I will tell you how to reverse the operation and factor these trinomials back into binomials.
ISAIAH LOPEZ
Do you know how to multiply an equation like this: (x+3)(x-2)? The answer would be x² - 2x + 3x - 6, which would then be simplified to x² + x - 6. If you don't know how to multiply two binomials like that then check out my previous article: Multiplying Binomials. When you multiply two binomials, like I did earlier, you get a trinomial. There is usually a reverse of everything, so you have to know how to factor a trinomial back into the two binomials multiplied to get it. So let's say you have x² + 5x - 6. The first step to factoring a trinomial is to just put the x in each binomial in parenthesis, (x )(x ), since you already know that both trinomials will start with an x. The next step is to list factors of the last number, which is called the constant. In our example, -6 can break into (-6 • 1), (6 • -1), (-2 • 3), and (-3 • 2). Then choose the set of factors that add up to make the middle term. The set (6 • -1) makes 5 when added. This is the right set. After that, put the set into your two binomials, like (x + 6)(x - 1). Keep in mind that any negative numbers will be written as x - that number.
Ok, so you are done now. If you want to check your work to make sure you have the right answer, then just simply add the constant in the binomials and if it adds up to the coefficient of the middle term, then you know you have the product of two binomials. So if you ever see a test or quiz that says write a trinomial as the product of two binomials, then just follow the steps and you should be right every time.