Lesson 3: Factoring Trinomials
In this lesson we begin our work factoring trinomials. As you will see, the better you are at multiplying binomials, the easier this lesson will be. For example, to factor x2 – x – 6, you first need to know that
(x – 3)(x + 2) = x2 – x – 6
If you don't understand the line above, then you need to review multiplication with polynomials, which is in Lesson 1. Everything you do here, even if it is going back to review multiplying polynomials, will help you with the next algebra course you take. It's simple: If you are working algebra problems, you are getting better at algebra.
Also, the work we did in the previous section will show up again here. The first step in any factoring problem is to factor out the greatest common factor. For example, to factor 5x2 – 5x – 30, the first step is to notice that there is a factor of 5 common to each term. Once you notice this, you can factor out the 5 and write
5x2 – 5x – 30 = 5(x2 – x – 6)
Then you can factor the trinomial inside the parentheses to get
5x2 – 5x – 30 = 5(x2 – x – 6) = 5(x – 3)(x + 2)
The last step is what you will learn how to do in this section.
Success Skill: Understanding, necessary?