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# Solutions

## Solutions to Try Its

1. $4{x}^{2}-8x+15-\frac{78}{4x+5}\\$ 2. $3{x}^{3}-3{x}^{2}+21x - 150+\frac{1,090}{x+7}\\$ 3. $3{x}^{2}-4x+1\\$

### Solutions to Odd-Numbered Exercises

1. The binomial is a factor of the polynomial. 3. $x+6+\frac{5}{x - 1}\text{,}\text{quotient:}x+6\text{,}\text{remainder:}\text{5}\\$ 5. $3x+2\text{,}\text{ quotient: }3x+2\text{, }\text{remainder: 0}\\$ 7. $x - 5\text{,}\text{quotient: }x - 5\text{,}\text{remainder: }\text{0}\\$ 9. $2x - 7+\frac{16}{x+2}\text{,}\text{quotient: }\text{ }2x - 7\text{,}\text{remainder: }\text{16}\\$ 11. $x - 2+\frac{6}{3x+1}\text{,}\text{quotient: }x - 2\text{,}\text{remainder: }\text{6}\\$ 13. $2{x}^{2}-3x+5\text{,}\text{quotient:}2{x}^{2}-3x+5\text{,}\text{remainder: }\text{0}\\$ 15. $2{x}^{2}+2x+1+\frac{10}{x - 4}\\$ 17. $2{x}^{2}-7x+1-\frac{2}{2x+1}\\$ 19. $3{x}^{2}-11x+34-\frac{106}{x+3}\\$ 21. ${x}^{2}+5x+1\\$ 23. $4{x}^{2}-21x+84-\frac{323}{x+4}\\$ 25. ${x}^{2}-14x+49\\$ 27. $3{x}^{2}+x+\frac{2}{3x - 1}\\$ 29. ${x}^{3}-3x+1\\$ 31. ${x}^{3}-{x}^{2}+2\\$ 33. ${x}^{3}-6{x}^{2}+12x - 8\\$ 35. ${x}^{3}-9{x}^{2}+27x - 27\\$ 37. $2{x}^{3}-2x+2\\$ 39. $\left(x - 1\right)\left({x}^{2}+2x+4\right)\\$ 41. $\left(x - 5\right)\left({x}^{2}+x+1\right)\\$ 43. $\text{Quotient: }4{x}^{2}+8x+16\text{,}\text{remainder: }-1\\$ 45. $\text{Quotient: }3{x}^{2}+3x+5\text{,}\text{remainder: }0\\$ 47. $\text{Quotient: }{x}^{3}-2{x}^{2}+4x - 8\text{,}\text{remainder: }-6\\$ 49. ${x}^{6}-{x}^{5}+{x}^{4}-{x}^{3}+{x}^{2}-x+1\\$ 51. ${x}^{3}-{x}^{2}+x - 1+\frac{1}{x+1}\\$ 53. $1+\frac{1+i}{x-i}\\$ 55. $1+\frac{1-i}{x+i}\\$ 57. ${x}^{2}-ix - 1+\frac{1-i}{x-i}\\$ 59. $2{x}^{2}+3\\$ 61. $2x+3\\$ 63. $x+2\\$ 65. $x - 3\\$ 67. $3{x}^{2}-2\\$