Lesson Summary: By the end of this lesson, students should be able to understand how and when to use synthetic and long division. One should know to only use synthetic division when one's divisor is linear. For long division, one should remember to divide, multiply, subtract, and finally to bring down. In addition, one should remember that when using either methods to divide polynomials, one should have no missing powers. Finally, when one becomes familiar with these two methods he or she should be able to apply them and understand the terminology. For example, when one sees multiplicity of 2 that means that there will be factor as a solution twice. In addition, one should be able to solve polynomials with irrational and complex roots.