Solutions 16: Dividing Polynomials

Solutions to Try Its

1. [latex]4{x}^{2}-8x+15-\frac{78}{4x+5}[/latex]

2. [latex]3{x}^{3}-3{x}^{2}+21x - 150+\frac{1,090}{x+7}[/latex]

3. [latex]3{x}^{2}-4x+1[/latex]

Solutions to Odd-Numbered Exercises

1. The binomial is a factor of the polynomial.

3. [latex]x+6+\frac{5}{x - 1}\text{,}\text{quotient:}x+6\text{,}\text{remainder:}\text{5}[/latex]

5. [latex]3x+2\text{,}\text{ quotient: }3x+2\text{, }\text{remainder: 0}[/latex]

7. [latex]x - 5\text{,}\text{quotient: }x - 5\text{,}\text{remainder: }\text{0}[/latex]

9. [latex]2x - 7+\frac{16}{x+2}\text{,}\text{quotient: }\text{ }2x - 7\text{,}\text{remainder: }\text{16}[/latex]

11. [latex]x - 2+\frac{6}{3x+1}\text{,}\text{quotient: }x - 2\text{,}\text{remainder: }\text{6}[/latex]

13. [latex]2{x}^{2}-3x+5\text{,}\text{quotient:}2{x}^{2}-3x+5\text{,}\text{remainder: }\text{0}[/latex]

15. [latex]2{x}^{2}+2x+1+\frac{10}{x - 4}[/latex]

17. [latex]2{x}^{2}-7x+1-\frac{2}{2x+1}[/latex]

19. [latex]3{x}^{2}-11x+34-\frac{106}{x+3}[/latex]

21. [latex]{x}^{2}+5x+1[/latex]

23. [latex]4{x}^{2}-21x+84-\frac{323}{x+4}[/latex]

25. [latex]{x}^{2}-14x+49[/latex]

27. [latex]3{x}^{2}+x+\frac{2}{3x - 1}[/latex]

29. [latex]{x}^{3}-3x+1[/latex]

31. [latex]{x}^{3}-{x}^{2}+2[/latex]

33. [latex]{x}^{3}-6{x}^{2}+12x - 8[/latex]

35. [latex]{x}^{3}-9{x}^{2}+27x - 27[/latex]

37. [latex]2{x}^{3}-2x+2[/latex]

39. [latex]\left(x - 1\right)\left({x}^{2}+2x+4\right)[/latex]

41. [latex]\left(x - 5\right)\left({x}^{2}+x+1\right)[/latex]

43. [latex]\text{Quotient: }4{x}^{2}+8x+16\text{,}\text{remainder: }-1[/latex]

45. [latex]\text{Quotient: }3{x}^{2}+3x+5\text{,}\text{remainder: }0[/latex]

47. [latex]\text{Quotient: }{x}^{3}-2{x}^{2}+4x - 8\text{,}\text{remainder: }-6[/latex]

49. [latex]{x}^{6}-{x}^{5}+{x}^{4}-{x}^{3}+{x}^{2}-x+1[/latex]

51. [latex]{x}^{3}-{x}^{2}+x - 1+\frac{1}{x+1}[/latex]

53. [latex]1+\frac{1+i}{x-i}[/latex]

55. [latex]1+\frac{1-i}{x+i}[/latex]

57. [latex]{x}^{2}-ix - 1+\frac{1-i}{x-i}[/latex]

59. [latex]2{x}^{2}+3[/latex]

61. [latex]2x+3[/latex]

63. [latex]x+2[/latex]

65. [latex]x - 3[/latex]

67. [latex]3{x}^{2}-2[/latex]