42. Use Descartes' rule of signs to determine the different possibilities for the numbers of positive, negative, and nonreal complex zeros of f(x)=x3+3x²-4x-2. 43. Is x + 1 a factor of f(x) = x3 + 2x² + 3x + 2? 44. Find a polynomial function f with real coefficients of degree 4 with 3, 1, and -1 + 3i as zeros, and f(2) = -36. 45. Find a polynomial function f of degree 3 with -2, 1, and 4 as zeros, and f(2) = 16. 46. Find all zeros of f(x) = x4 - 3x38x2 + 22x24, given that 1 + i is a zero. 47. Find all zeros of f(x) = 2x4x3 + 7x² - 4x4, given that 1 and -2i are zeros. 48. Find a value of k such that x - 4 is a factor of f(x) = x³- 2x² + kx +4. 49. Find a value of k such that when the polynomial x³-3x² + kx-4 is divided by x-2, the remainder is 5. 50. Give the maximum number of turning points of the graph of each function. (a) f(x)=x³-9x2 (b) f(x)=4x³-6x2 +2 51. Concept Check Give an example of a cubic polynomial function having exactly one real zero, and then sketch its graph. A↑ 99 Chegg: College Algebra Graph each polynomial function. 55. f(x)=(x-2)²(x+3) 57. f(x)=2x3 + x² - x 59. f(x)=x+x³-3x² - 4x-4 -2x+7x-2x-3 Tiger Algebra Solv 56. f(x) = -2x3 + 7x² - 2x - 3 58. f(x)=x-3x²+2 60. f(x) = -2x+7x³- 4x² - 4x Concept Check For each polynomial function, identify its graph from choices A-F 61. f(x)=(x-2)²(x-5) 62. f(x)=-(x-2)²(x-5) 63. f(x)=(x-2)2(x-5)² 65. f(x)=-(x-2)(x-5) A. y B. y D. 0 2 k X 5 E. 64. f(x)=(x-2)(x-5) 66. f(x)=-(x-2)²(x-5)² C. 0 2 ·A· F 5