Computer algebra systems are being used more and more frequently in mathematics courses of all levels. For instructors to use these systems effectively, they need to have an idea of how the systems work. To illuminate the mechanics, the implementation of a simple computer algebra system will be described. Further, if instructors understand the methods used by computers, they may find the ideas involved useful for human students even without computers. A lesson plan will be described that is aimed at students with little or no algebra background followed by a discussion of the author's experience using this lesson in the classroom.
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