Solving Cubic Equations using the Factor Theorem

Solve simple cubic equations having at least one integer root by using the Factor Theorem, reducing to a quadratic by comparing coefficients, and then finding the two remaining roots.

Author and programmer: Ron Barrow

UK Years 12-13, Ages 16-19, KS5, Core AS and A2 Mathematics - Functions and Graphs
US Grades 11, 12 - Algebra I and Algebra II


Instructions below   See also:  Polynomial Graphs   Polynomial Transformations

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How to Use this Applet

When you start the screen, a simple cubic equation is written for you to solve. What's simple about it? Well, the coefficient of the cubed term is 1, and there is one solution which is an integer between -5 and +5.
At the first step you have to find this integer root, by trying different values of A (press the 'A+' or 'A-' button). Notice that finding this root involves using the Factor Theorem.

Once you've done this you move on to further steps in the calculation, which is mostly done for you. After you've got your other solutions (if they exist), a graph of the function is drawn, so that you can see how the solutions relate to the graph. The purpose of this program is to help you understand the process of finding solutions to this type of cubic equation. Enjoy and learn!