Do problems: 7, 9, 15, 17, 19, 23, 27, 33, 35, 41, 43, 57, 58

Please show all work and do it on paper if possible

Algebraic For the following exercises, use the Remainder Theorem to find the remainder. 6. (x4 - 9x2+ 14) + (x - 2) 7. (3x3 - 2x2 + x - 4) + (x+ 3) 8. (x4 + 5x3 - 4x - 17) + (x +1) 9. (-3x2 + 6x + 24) + (x - 4) 10. (5x5 - 4x4 + 3x3 - 2x2 + x - 1) + (x+6) 11. (x4 - 1) + (x - 4) 12. (3x3 + 4x2 - 8x + 2) + (x - 3) 13. (4x3 + 5x2 - 2x + 7) + (x+2) For the following exercises, use the Factor Theorem to find all real zeros for the given polynomial function and one factor. 14. f(x) = 2x3 - 9x2 + 13x - 6; x -1 15. f(x) = 2x3 + x2 - 5x + 2; x+2 16. f (x) = 3x3 + x2 - 20x + 12; x + 3 17. f(x) = 2x3 + 3x2+ x+6; x+2 18. f(x) = -5x3 + 16x2 - 9; x -3 19. x3 + 3x2 + 4x + 12; x + 3 20. 4x3 - 7x + 3; x - 1 21. 2x3 + 5x2 - 12x - 30, 2x + 5For the following exercises, use the Rational Zero Theorem to find all real zeros. 22. x3 - 3x2 - 10x + 24 = 0 23. 2x3 + 7x2 - 10x - 24 = 0 24. x3 + 2x2 - 9x - 18 = 0 25. x3 + 5x2 - 16x - 80 = 0 26. x3 - 3x2 - 25x + 75 = 0 27. 2x3 - 3x2 - 32x - 15 = 0 28. 2x3 + x2 - 7x - 6 = 0 29. 2x3 - 3x2 - x + 1 = 0 30. 3x3 - x2 - 11x - 6 = 0 31. 2x3 - 5x2 + 9x - 9 = 0 32. 2x3 - 3x2 + 4x + 3 = 0 33. x4 - 2x3 - 7x2 + 8x + 12 = 0 34. x4 + 2x3 - 9x2 - 2x + 8 = 0 35. 4x4 + 4x3 - 25x2 - x + 6 = 0 36. 2x4 - 3x3 - 15x2 + 32x - 12 = 0 37. x4+ 2x3 - 4x2 - 10x - 5 = 0 38. 4x3 - 3x + 1 = 0 39. 8x + 26x3+ 39x2 + 26x +6For the following exercises, find all complex solutions (real and non-real). 40. x3 + x2 + x+1 = 0 41. x3 - 8x2 + 25x - 26 = 0 42. x3 + 13x2 + 57x + 85 = 0 43. 3x3 - 4x2 + 11x + 10 = 0 44. x4 + 2x3+ 22x2 + 50x - 75 = 0 45. 2x3 - 3x2 + 32x + 17 = 0Numeric For the following exercises, list all possible rational zeros for the functions. 56. f(x) = x4 + 3x3 - 4x + 4 57. f(x) = 2x' + 3x2 - 8x +5 58. f (x) = 3x + 5x2 - 5x + 4 59. f (x) = 6x4 - 10x2 + 13x + 1 60. f (x) = 4x5 - 10x4 + 8x3 + x2 - 8