Solutions

Solutions to Try Its

1. 
4x28x+15784x+54{x}^{2}-8x+15-\frac{78}{4x+5}


2. 
3x33x2+21x150+1,090x+73{x}^{3}-3{x}^{2}+21x - 150+\frac{1,090}{x+7}


3. 
3x24x+13{x}^{2}-4x+1


Solutions to Odd-Numbered Exercises

1. The binomial is a factor of the polynomial.

3. 
x+6+5x1,quotient:x+6,remainder:5x+6+\frac{5}{x - 1}\text{,}\text{quotient:}x+6\text{,}\text{remainder:}\text{5}


5. 
3x+2, quotient: 3x+2, remainder: 03x+2\text{,}\text{ quotient: }3x+2\text{, }\text{remainder: 0}


7. 
x5,quotient: x5,remainder: 0x - 5\text{,}\text{quotient: }x - 5\text{,}\text{remainder: }\text{0}


9. 
2x7+16x+2,quotient:  2x7,remainder: 162x - 7+\frac{16}{x+2}\text{,}\text{quotient: }\text{ }2x - 7\text{,}\text{remainder: }\text{16}


11. 
x2+63x+1,quotient: x2,remainder: 6x - 2+\frac{6}{3x+1}\text{,}\text{quotient: }x - 2\text{,}\text{remainder: }\text{6}


13. 
2x23x+5,quotient:2x23x+5,remainder: 02{x}^{2}-3x+5\text{,}\text{quotient:}2{x}^{2}-3x+5\text{,}\text{remainder: }\text{0}


15. 
2x2+2x+1+10x42{x}^{2}+2x+1+\frac{10}{x - 4}


17. 
2x27x+122x+12{x}^{2}-7x+1-\frac{2}{2x+1}


19. 
3x211x+34106x+33{x}^{2}-11x+34-\frac{106}{x+3}


21. 
x2+5x+1{x}^{2}+5x+1


23. 
4x221x+84323x+44{x}^{2}-21x+84-\frac{323}{x+4}


25. 
x214x+49{x}^{2}-14x+49


27. 
3x2+x+23x13{x}^{2}+x+\frac{2}{3x - 1}


29. 
x33x+1{x}^{3}-3x+1


31. 
x3x2+2{x}^{3}-{x}^{2}+2


33. 
x36x2+12x8{x}^{3}-6{x}^{2}+12x - 8


35. 
x39x2+27x27{x}^{3}-9{x}^{2}+27x - 27


37. 
2x32x+22{x}^{3}-2x+2


39. 
(x1)(x2+2x+4)\left(x - 1\right)\left({x}^{2}+2x+4\right)


41. 
(x5)(x2+x+1)\left(x - 5\right)\left({x}^{2}+x+1\right)


43. 
Quotient: 4x2+8x+16,remainder: 1\text{Quotient: }4{x}^{2}+8x+16\text{,}\text{remainder: }-1


45. 
Quotient: 3x2+3x+5,remainder: 0\text{Quotient: }3{x}^{2}+3x+5\text{,}\text{remainder: }0


47. 
Quotient: x32x2+4x8,remainder: 6\text{Quotient: }{x}^{3}-2{x}^{2}+4x - 8\text{,}\text{remainder: }-6


49. 
x6x5+x4x3+x2x+1{x}^{6}-{x}^{5}+{x}^{4}-{x}^{3}+{x}^{2}-x+1


51. 
x3x2+x1+1x+1{x}^{3}-{x}^{2}+x - 1+\frac{1}{x+1}


53. 
1+1+ixi1+\frac{1+i}{x-i}


55. 
1+1ix+i1+\frac{1-i}{x+i}


57. 
x2ix1+1ixi{x}^{2}-ix - 1+\frac{1-i}{x-i}


59. 
2x2+32{x}^{2}+3


61. 
2x+32x+3


63. 
x+2x+2


65. 
x3x - 3


67. 
3x223{x}^{2}-2


Licenses and Attributions