Factoring Trinomials

Lesson 3 in the "Factoring Series"

Factoring trinomials is probably the most common type of factoring in Algebra. In Algebra 1 we will factor trinomials that have a lead coefficient of 1. In Algebra 2, we will progress to factoring more complex trinomials whose lead coefficient is greater than 1.

To begin this lesson, it is important for you to understand the process of multiplying binomials using the FOIL method. Please be sure to review that lesson before starting this lesson. Click here to review the FOIL method lesson.

The diagram below outlines the product of multiplying two binomials. It's important to understand how we reach the trinomial because in this lesson we are going to work backwards to form the factors or two binomials.

Result of Multiplying Two Binomials

Ok, now let's work backwards. You will be given the trinomial and in order to factor the trinomial, you will need to work backwards to find the two binomials. Let's look at an example.

Example 1

Just 3 easy steps to factoring trinomials. Let's take a look at another example. This example is a little more difficult because we will be working with negative and positive numbers.

Example 2

I know that factoring trinomials is tough, so let's look at one more example. Again, this trinomial will contain a minus sign, so pay careful attention to the positive and negative numbers that you choose.

Example 3

Are you ready to practice a couple on your own?

Practice Problems

Factor the following trinomials:

1. x² +x - 20

2. x² - 11x + 18

Answer Key

Problem 1

Problem 2

Great Job! You have completed the Algebra 1 Polynomials Unit!