Using the Greatest Common Factor to Solve Cubic Equations

Using the Greatest Common Factor to Solve Cubic Equations
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  • 0:54 Factoring the GCF
  • 2:12 Using the GCF Method
  • 2:54 Finding the Solutions
  • 3:27 Lesson Summary
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Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson to learn how to identify the cubic equations for which you can factor out the greatest common factor to help you solve them. Learn the steps you need to take to solve them.

Cubic Equations

Cubic equations, equations with a degree of 3, are useful types of equations. One of the most useful applications is that of volumes. This is why mathematicians over the years have come up with several methods to solve them, and this is why it is also important for you to learn how to solve them. But because the mathematicians from before have already given you a head start by giving you some tools that work, your work has become a lot easier.

In this video lesson, we're going to learn how to factor out the greatest common factor to help us solve cubic equations. However, we also need to recall our skills in finding the greatest common factor as well as our skills in solving quadratic equations. If you feel you are a bit rusty, take a moment to pause this video while you refresh. Come back when you are ready, and we will be good to go!

Factoring Out the Greatest Common Factor

I want to briefly give you a quick overview of this method. Your first step is to identify the greatest common factor. Recall that your greatest common factor is a value that you can take out of every single term in your equation.

Once you have identified your greatest common factor, your next step is to factor your cubic equation by using it. You will be left with your greatest common factor multiplied by a quadratic.

At this point, you will use your quadratic equation solving skills to finish finding your two other solutions. Set your greatest common factor that you just factored out to equal zero to find one of the solutions to your cubic equation.

Only certain types of cubic equations are suitable for using this method, however. It is the type that doesn't have a constant term. For example, the cubic equation x^3 + 2x^2 + 4x = 0 can be solved by factoring out the greatest common factor, while the cubic equation x^3 + 4x + 3 = 0 needs a different method to solve it. Notice how the one where you can use this method doesn't have a constant term, while the one that needs a different method does?

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