Figuring Out the Quadratic Formula

Going for the greatest common factor. Another type of cubic equation that’s easy to solve is one in which you can factor out a variable greatest common factor (GCF), leaving a second factor that is linear or quadratic (first or second degree). You apply the MPZ and work to find the solutions — usually three of them.

Factoring out a first-degree variable GCF When the terms of a three-term cubic equation all have the same first-degree variable as a factor, then factor that out. The resulting equation will have the variable as one factor and a quadratic expression as the second factor. The first-degree variable will always give you a solution of 0 when you apply the MPZ. If the quadratic has solutions, you can find them using the methods in Chapter 13.

Solving the first equation involves taking the square root of each side of the equation. This process usually results in two different answers — the positive answer and the negative answer. However, this isn’t the case with w2 = 0 because 0 is neither positive nor negative. So there’s only one solution from this factor: w = 0. And the other factor gives you a solution of w = 3. So, even though this is a cubic equation, there are only two solutions to it.


Grouping is a form of factoring that you can use when you have four or more terms that don’t have a single greatest common factor. These four or more terms may be grouped, however, when pairs of the terms have factors in common. The method of grouping is covered in Chapter 8. I give you one example here, but turn to Chapter 8 for a more complete explanation.

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