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.
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.
Did you notice how we added the two last terms of each binomial (3 & 5) to get the middle term and we multiplied the same two last terms (3 & 5) in order to get the last term of the trinomial?
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.
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.
When you have a trinomial with a minus sign, pay careful attention to your positive and negative numbers. In the example above, 8 and -2 are the numbers that we needed to complete our binomials; however, -8 and 2 would not have worked!
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.
Enter your expression and click "Factor".
Great Job! You have completed the Algebra 1 Polynomials Unit!
- Introduction to Polynomials (Definitions)
- Adding Polynomials
- Subtracting Polynomials
- Multiplying Polynomials
- Using the FOIL Method to Multiply Binomials
- Squaring a Binomial - Using a Special Rule
- Difference of Two Squares - "Special Binomials"
- Factoring Polynomials
Using the Greatest Common Factor (GCF)
- Factoring Polynomials by Grouping
- Factoring Trinomials with a Lead Coefficient
Greater than One
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