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Study Guides > MATH 1314: College Algebra

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\\

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