Patrick Just Math Tutorials: "Long Division of Polynomials" Consider the rational expressions: (x-1)/(x-1), (x^2 - 1) / (x -1), (x^3 - 1)/ (x-1), and (x^4 -1)/ (x-1). Do you see a pattern when simplifying them through either long or synthetic division? Generalizing, do you think (x^n - 1) / (x - 1) simplifies to a pattern, for n >=1? Why or why not? How could you use long or synthetic division to investigate?

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