Please help! 27-36 all!

46. f(x) = x5 - x4+ 21x2 + 19x -3 In Exercises 27-30, find the polynomial function with leading coeffi- cient 2 that has the given degree and zeros. 27. Degree 3, with -2, 1, and 4 as zeros TITTITTIT 28. Degree 3, with - 1, 3, and -5 as zeros 29. Degree 3, with 2, 2, and 2 as zeros 30. Degree 4, with -3, -1, 0, and ? as zeros In Exercises 31 and 32, using only algebraic methods, find the cubic function with the given table of values. Check with a grapher. 31. x -4 [-5, 5] by [-1000, 1000] f (x ) 0 180 0 32. 47. f(x) = x5 - 4x4 - 129x5 + 396.x2 -8x + 3 f (x) 24 TITTY In Exercises 33-36, use the Rational Zeros Theorem to write a list of all potential rational zeros. Then determine which ones, if any, are zeros. 33. f(x) = 6x3 - 5x - 1 34. f (x) = 3x3 - 7x2 + 6.x - 14 35. f(x) = 2x3 - x2 -9x +9 36. f(x) = 6x4 - x3 - 6x2 - x - 12 [-5, 5] by [-1000, 1000] In Exercises 37-40, use synthetic division to prove that the number k is an upper bound for the real zeros of the function f. 37. k = 3; f(x) = 2x3 - 4x2 + x-2 48. f(x) = 2x5 - 5x4 - 141x3 + 216x2 - 91x + 25 38. k = 5; f(x) = 2x3-5x2 -5x - 1 39. k = 2; f(x) = x4- x3+ x+ x- 12 40. k = 3; f(x) = 4x4 -6x3 -7x2 + 9x + 2 In Exercises 41-44, use synthetic division to prove that the number k is a lower bound for the real zeros of the function f. 41. k = -1; f(x) = 3x3 - 4x2 + x+ 3 42. k = -3; f(x) = x3+2x2 + 2x + 5 43. k = 0;f(x) =x3 -4x2+7x -2 [-5, 5] by [-1000, 1000] 44. k = -4; f(x) = 3x3 - x2 - 5x -3 In Exercises 45-48, use the upper and lower bound tests to decide In Exercises 49-56, find all of the real zeros of the function, fin whether there could be real zeros for the function outside the window values whenever possible. Identify each zero as rational or irrati shown. If so, check for additional zeros. 49. f(x) = 2x3 - 3.x2 - 4x + 6 45. f(x) = 6x4 - 11x3-7x2 + 8x - 34 50. f(x) = x3 + 3.12 - 3.x -9 51. f (x) = 1+ 12 - 8x -6 52. f (x) = 13 - 612 + 7.x + 4 53. f(x) = 14 - 3.13 - 612 + 6x + 8 54. f (x ) = 14 - 13 - 7x2 + 5x + 10 55. f(x) = 2x4 - 7x3 - 2x2 - 7x - 4 56. f (x) = 3.x4 - 283 + 3x2 + x - 2 [-5, 5] by [-200, 1000]