EXERCISES Practice Divide using synthetic division. 14. (x2 + 20x + 91) + (x + 7) 15. (x3 - 9x2 + 27x - 28) + (x - 3) 16. (x4 + x3 - 1) + (x - 2) 17. (x4 - 8x2 + 16) + (x + 2) 18. (3x4 - 2x3 + 5x2 - 4x - 2) + (x + 1) 19. (2x3 - 2x - 3) + (x - 1) Use the Remainder Theorem to find the remainder for each division. State whether the binomial is a factor of the polynomial. 20. (x2 - 2) + (x - 1) 21. (x5 + 32) + (x + 2) 22. (x4 - 6x2 + 8) + (x - V2) 23. (x3 - x + 6) + (x - 2) 24. (4x3 + 4x' + 2x + 3) + (x - 1) 25. (2x3 - 3x' + x) + (x - 1) 226 Chapter 4 Polynomial and Rational Functions www.amc.glencoe.com/self_check_quiz CONTENTS 26. Which binomial is a factor of the polynomial x3 + 3x2 - 2x - 8? a. x- 1 b. x+ 1 C. x - 2 d. x + 2 27. Verify that x - V 6 is a factor of x* - 36. 28. Use synthetic division to find all the factors of x3 + 7x2 - x - 7 if one of the factors is x + 1. Determine the binomial factors of each polynomial. 29. x3 + x2 - 4x - 4 30. x3 - x2 - 49x + 49 31. x3 - 5x2 + 2x + 8 32. x3 - 2x2 - 4x + 8 33. x3 + 4x- - x - 4 34. x3 + 3x2 + 3x + 1 35. How many times is 2 a root of x6 - 9x4 + 24x2 - 16 = 0? 36. Determine how many times -1 is a root of x3 + 2x2 - x - 2 = 0. Then find the other roots. Find the value of k so that each remainder is zero. 37. (2x3 - x2+ x+ k) + (x -1) 38. (x3 - kx2 + 2x - 4) + (x - 2) 39. (x3 + 18x2 + kx + 4) + (x + 2) 40. (x3 + 4x2 - kx + 1) + (x + 1)