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1.1. a. What is a rational expression? How would symbolize a rational expression? sinx x24 b. Explain why is not a rational expression. c. Explain the difference between a proper versus improper rational expression. 2.2. x34x2x+5 a. Carry out the division 2 x x+1 and write your answer in a form given by the Division algorithm. 3x2 x325 x5+x3x+1 c. Carry out the division T using synthetic division and write your answer in a form given by the Division Algorithm. d. Explain why synthetic division would not work in partial. 3.C. a. Explain what a linear factor is. Give two examples of such. b. Explain what an irreducible quadratic factor is. Give two examples of such. b. Carry out the division and write your answer in a form given by the Division aigorithm. 4.C. When integrating a rational expression, symbolically we write I 3:; dx. What is your first step if the degree of N(x) is greater than or equal to the degree of DOC)? 3 . x +2x 5.3. Find f x+1 dx HELP: the integrand is an improper fraction so divide the polynomials first 2 x +x3 6.4. Find f dx x32x28x x25x+1 7.6. Consider the rational function W where some ofthe linearfactors x (Jr1) (x+1) repeat. Write out its partial fraction expansion with undetermined coefficients but don't determine the values of the coefficients (since this would take a long time to accomplish} x4x23x+2 8.7. Find 1.de HELP: the fraction is improper so what do before a partial fraction expansion? 9.8. Classify each quadratic polynomial as reducible or irreducible over the real numbers. If reducible then factor it. a. 2x2 13x 7 c. y2 + y + 3 d. it2 + 1 d. 25t2 4