1. 16x3y + 0,25yz3
ĐS: 1/4y(4x + z)(16x2- 4xz + z2)
2. x 4 – 4x3 + 4x2
ĐS: x2(x - 2)2
3. 2ab2 – a2b – b3
ĐS: - b(a- b)2
4. a 3 + a2b – ab2 – b3
ĐS: (a-b)(a+b)2
5. x 3 + x2 – 4x – 4
ĐS: (x+1)(x+2)(x-2)
6. x 3 – x2 – x + 1
ĐS: (x-1)2(x+1)
7. x 4 + x3 + x2 – 1
ĐS: (x+1)(x3 +x-1)
8. x 2y2 + 1 – x2 – y2
ĐS: (x+1)(x-1)(y+1)(y-1)
10. x 4 – x2 + 2x – 1
ĐS : (x2-x+1)(x2+x+1)
11. 3a – 3b + a2 – 2ab + b2
(a-b)(3+a-b)
12. a 2 + 2ab + b2 – 2a – 2b + 1
ĐS: (a+b-1)2
Bài tập phân tích đa thức thành nhân tử 1. 16x3y + 0,25yz3 ĐS: 1/4y(4x + z)(16x2- 4xz + z2) 59. (a + b + c)2 + (a + b – c)2 – 4c2 ĐS: 2(a+b+c)(a+b-c) 2. x 4 – 4x3 + 4x2 ĐS: x2(x - 2)2 60. 4a2b2 – (a2 + b2 – c2)2 ĐS: (a+b-c)(a+b+c) (c+a-b)(c-a+b) 3. 2ab2 – a2b – b3 ĐS: - b(a- b)2 61. a 4 + b4 + c4 – 2a2b2 – 2b2c2 – 2a2c2 ĐS: (a+b+c) (a-b-c) (a+b-c) (a-b+c) 4. a 3 + a2b – ab2 – b3 ĐS: (a-b)(a+b)2 62. a(b3 – c3) + b(c3 – a3) + c(a3 – b3) ĐS: 5. x 3 + x2 – 4x – 4 ĐS: (x+1)(x+2)(x-2) 63. a 6 – a4 + 2a3 + 2a2 ĐS: a2(a+1)2(a2-2a+2) 6. x 3 – x2 – x + 1 ĐS: (x-1)2(x+1) 64. (a + b)3 – (a – b)3 ĐS: 2b(3a2+b2) 7. x 4 + x3 + x2 – 1 ĐS: (x+1)(x3 +x-1) 65. x 3 – 3x2 + 3x – 1 – y3 ĐS: (x-y-1)(x2-2x+1+xy-y+y2) 8. x 2y2 + 1 – x2 – y2 ĐS: (x+1)(x-1)(y+1)(y-1) 66. x m + 4 + xm + 3 – x – 1 ĐS: (x+1)(xm+3-1) 10. x 4 – x2 + 2x – 1 ĐS : (x2-x+1)(x2+x+1) 67. (x + y)3 – x3 – y3 ĐS: 3xy(x+y) 11. 3a – 3b + a2 – 2ab + b2 (a-b)(3+a-b) 68. (x + y + z)3 – x3 – y3 – z3 ĐS: 3(x+y)(y+z)(z+x) 12. a 2 + 2ab + b2 – 2a – 2b + 1 ĐS: (a+b-1)2 69. (b – c)3 + (c – a)3 + (a – b)3 ĐS: 3(a-b)(b-c)(c-a) 13. a 2 – b2 – 4a + 4b ĐS: (a-b)(a+b-4) 70. x3 + y3+ z3 – 3xyz ĐS: (x+y+z)(x2+y2+z2-xy-yz-zx) 14. a 3 – b3 – 3a + 3b ĐS: (a-b)(a2+ab+b2-3) 71. (x + y)5 – x5 – y5 ĐS: 5xy(x+y)(x2+3xy+y2) 15. x 3 + 3x2 – 3x – 1 ĐS: (x-1)(x2+4x+1) 72. (x2 + y2)3 + (z2 – x2)3 – (y2 + z2)3 ĐS: 3(x2+y2)(y2+z2)(x-z)(x+z) 16. x 3 – 3x2 – 3x + 1 ĐS: (x+1)(x2- 4x+1) 73 ab(a + b) + bc(b + c) + ca(c + a) + abc ĐS: 17. x 3 – 4x2 + 4x – 1 ĐS: (x-1)(x2- 3x+1) 74 (x + y + z)5 – x5 – y5 – z5 ĐS: 5(x+y)(y+z)(z+x)(x2+y2+z2+xy+yz+zx) 18. 4a2b2 – (a2 + b2 – 1)2 ĐS: (1-a+b)(1+a-b)(a+b-1)(a+b+1) 75 a(b2 + c2) + b(c2 + a2) + c(a2 + b2) + 2abc ĐS: (a+b)(b+c)(c+a) 19. (xy + 4)2 – (2x + 2y)2 ĐS: (x+2)(x-2)(y+2)(y-2) 76 a3(b – c) + b3(c – a) + c3(a – b) ĐS: (a-b)(a-c)(b-c)(a+b+c) 20. (a2 + b2 + ab)2 – a2b2 – b2c2 – c2a2 ĐS:(a2+b2)(a+b+c)(a+b-c) 77 abc – (ab + bc + ac) + (a + b + c) – 1 ĐS: (a-1)(b-1)(c-1) 21. x2 – 6x + 8 ĐS(B21):(x-2)(x-4) 78. x3 – 5x2y – 14xy2 ĐS(B78): x(x+2y)(x-7y) 22 x2 – 7xy + 10y2 ĐS: (x-2y)(x-5y) 79. x4 – 7x2 + 1 ĐS: (x2-3x+1)(x2+3x+1) 23 a2 – 5a – 14 ĐS: (a-7)(a+2) 80. 4x4 – 13x2 + 1 ĐS: (x-2y)( 24 2m2 + 10m + 8 ĐS: 2(m+1)(m+4) 81. x2 + 8x + 7 ĐS: (x+7)(x+1) 25 4p2 – 36p + 56 ĐS: 4(p-7)(p-2) 82. x2 – 13x + 36 ĐS: (x-4)(x-9) 26 x3 – 5x2 – 14x ĐS: x(x-7)(x+2) 83. x2 + 3x – 18 ĐS: (x+6)(x-3) 27 a4 + a2 + 1 ĐS: (a2+a+1)(a2- a+1) 84. x2 – 5x – 24 ĐS: (x-8)(x+3) 28 a4 + a2 – 2 ĐS: (a-1)(a+1)(a2+2) 85. 3x2 – 16x + 5 ĐS: (x-5)(3x-1) 29 x4 + 4x2 + 3 ĐS: (x2+1)(x2+3) 86. 8x2 + 30x + 7 ĐS: (2x+7)(4x+1) 30. x3 – 10x – 12 ĐS: (x+2)(x2-2x-6) 87. 2x2 – 5x – 12 ĐS: (x-4)(2x+3) 31. x3 – 7x – 6 ĐS: (x+1)(x+2)(x-3) 88. 6x2 – 7x – 20 ĐS : (3x+4)(2x-5) 32. x2 – 7x + 12 ĐS: (x-3)(x-4) 89. x2 – 7x + 10 ĐS: (x-2)(x-5) 33. x2 – 5x – 14 ĐS: (x+2)(x-7) 90. x2 – 10x + 16 ĐS: (x-2)(x-8) 34. 4 x2 – 3x – 1 ĐS: (x-1)(4x+1) 91. 3x2 – 14x + 11 ĐS: (x-1)(3x-11) 35. 3 x2 – 7x + 4 ĐS: (x-1)(3x-4) 92. 5x2 + 8x – 13 ĐS: (x-1)(5x+13) 36. 2 x2 – 7x + 3 ĐS: (2x-1)(x-3) 93. x2 + 19x + 60 ĐS: (x+4)(x+15) 37. 6x3 – 17x2 + 14x – 3 ĐS: (x-1)(3x-1)(2x-3) 94. x4 + 4x2 – 5 ĐS: (x-1)(x+1)(x2-5) 38. 4x3 – 25x2 – 53x – 24 ĐS: (x+1)(x-8)(4x+3) 95. x3 – 19x + 30 ĐS: (x-2)(x-3)(x+5) 39. x4 – 34x2 + 225 ĐS: (x+3)(x-3)(x+5)(x-5) 96. x3 + 9x2 + 26x + 24 ĐS: (x+3)(x+2)(x+4) 40. 4x4 – 37x2 + 9 ĐS: ((x+3)(x-3)(2x+1)(2x-1) 97. 4x2 – 17xy + 13y2 ĐS: (x-y)(4x-13y) 41. x4 + 3x3 + x2 – 12x – 20 ĐS: (x-2)(x+2)(x2+3x+5) 98. - 7x2 + 5xy + 12y2 ĐS: (x+y)(12y-7x) 42. 2x4 + 5x3 + 13x2 + 25x + 15 ĐS:(B42) (x+1)(2x3+3x2+10x+15) 99. x3 + 4x2 – 31x - 70 ĐS:(B99): (x+2)(x-5)(x+7) 43 x4 + x2 + 1 ĐS: (x2-x+1)(x2+x+1) 100. x5 - x4 – 1 ĐS: (x3-x-1)(x2-x+1) 44 x4 – 3x2 + 9 ĐS: ( 101 x12 – 3x6 + 1 ĐS: (x6+x3-1)(x6-x3-1) 45 x4 + 3x2 + 4 ĐS: (: (x2-x+2)(x2+x+2) 102 x8 - 3x4 + 1 ĐS: (x4-x2-1)(x4+x2-1) 46 2x4 – x2 – 1 ĐS: (x+1)(x-1)(2x2+1) 103 a5 + a4 + a3 + a2 + a + 1 ĐS: (a2-a+1) (a2+a+1)(a+1) 47 x4y4 + 4 ĐS: (x2y2+2xy+2) (x2y2- 2xy+2) 104 m3 – 6m2 + 11m – 6 ĐS: (m-1)(m-2)(m-3) 48 x4y4 + 64 ĐS: (x2y2+4xy+8) (x2y2-4xy+8) 105 x4 + 6x3 + 7x2 – 6x + 1 ĐS: (x2+3x-1)2 49 4 x4y4 + 1 ĐS: (2x2y2-2xy+1) (2x2y2+2xy+1) 106 x3 + 4x2 – 29x + 24 ĐS: (x-1)(x-8)(x+3) 50 32x4 + 1 ĐS: ( 107 x10 + x8 + x6 + x4 + x2 + 1 ĐS:( x2+1) (x4-x2+1) (x2-x+1) (x2+x+1) 51 x4 + 4y4 ĐS: (x2- 2xy+2y2) (x2+ 2xy+2y2) 108 x7 + x5 + x4 + x3 + x2 + 1 ĐS: (x+1)(x6- x5+2 x4-x3+2x2-x+1) 52. x7 + x2 + 1 ĐS: (x2+x+1)(x5-x4+x2-x+1) 109 x5 – x4 – x3 – x2 – x – 2 ĐS: ( 53. x8 + x + 1 ĐS:( x2+x+1)(x6-x5+x3-x2+1) 110 x8 + x6 + x4 + x2 + 1 ĐS: ( 54. x8 + x7 + 1 ĐS: (x2+x+1)(x6-x4+x3-x+1) 111 x9 – x7 – x6 – x5 + x4 + x3 + x2 + 1 ĐS: ( 55. x8 + 3x4 + 1 ĐS: ( 112 a(b3 – c3) + b(c3 – a3) + c(a3 – b3) ĐS: (a-b)(b-c)(c-a)(a+b+c) 56. x10 + x5 + 1 ĐS: (x2+x+1)(x8-x7+x5- x4+x3- x+1) 113 4(x2 + 15x + 50)(x2 + 18x + 72) – 3x2 ĐS: ( 57. x5 + x + 1 ĐS: (x2+x+1)(x3-x2+1) 114 (x2 + x)2 + 4(x2 + x) – 12 ĐS: ( 58. x5 + x4 + 1 ĐS : (x2+x+1)(x3-x+1) 115 (x + y)7 – x7 – y7 116. x2 + 2xy – 8y2 + 2xz + 14yz – 3z2 133. (x + 2)(x + 4)(x + 6)(x + 8) + 16 ĐS: (x+4y-z)(x-2y+3z) ĐS: (x2+x+20)2 117. 3x2 – 22xy – 4x + 8y + 7y2 + 1 134. x4 – 6x3 + 7x2 + 6x – 8 ĐS: (3x-y-1)(x-7y-1) ĐS: (x-1) (x-2) (x+1) (x-4) 118. 12x2 + 5x – 12y2 + 12y – 10xy – 3 135. x3 + 9x2 + 26x + 24 ĐS: (3x+2y-1)(4x-6y+3) ĐS: (x+2) (x+3) (x+4) 119. 2x2 – 7xy + 3y2 + 5xz – 5yz + 2z2 136. ab(a – b) + bc(b – c) + ca(c – a) ĐS: (x-3y+2z)(2x-y+z) ĐS: (a-b)(b-c)(a-c) 120. x2 + 3xy + 2y2 + 3xz + 5yz + 2z2 137. a(b2 – c2) – b(a2 – c2) + c(a2 – b2) ĐS:(B120) (x+2y+z)(x+y+2z) ĐS(B137): b(a-c)(b-a-c) 121. x2 – 8xy + 15y2 + 2x – 4y – 3 138. (x – y)5 + (y – z)5 + (z – x)5 ĐS: (3x-y-1)(x-5y+3) ĐS: 122. x4 – 13x2 + 36 139. (x2 + x)2 + 4x2 + 4x – 12 (bỏ) ĐS: (x-2)(x+2)(x-3)(x+3) ĐS: (x2+x-2) (x2+x+6) 123. x4 + 3x2 – 2x + 3 140. (x2 + 4x + 8)2 + 3x(x2 + 4x + 8) + 2x2 ĐS: (x2+x+3) (x2-x+1) ĐS: (x2+5x+8)(x+2)(x+4) 124. x4 + 2x3 + 3x2 + 2x + 1 141. (x + 1)(x + 2)(x + 3)(x + 4) – 24 ĐS: ĐS: x(x+5)(x2+5x+10) 125. (a – b)3 + (b – c)3 + (c – a)3 (bỏ) 142. (x2 + 2x)2 + 9x2 + 18x + 20 ĐS: 3(a-b)(b-c)(c-a) ĐS: (x2+2x+4) (x2+2x+5) 126. (a – x)y3 – (a – y)x3 – (x – y)a3 143. x2 – 4xy + 4y2 – 2x + 4y – 35 ĐS: ĐS: (x-2y+5)(x-2y-7) 127. x(y2 – z2) + y(z2 – x2) + z(x2 – y2) ĐS: (x-y)(y-z)(z-x) 129. 3x5 – 10x4 – 8x3 – 3x2 + 10x + 8 ĐS: (x-1)( )( ) 130. 5x4 + 24x3 – 15x2 – 118x + 24 ĐS: (x-2)(5x3+34x2+53x-12) 131. 15x3 + 29x2 – 8x – 12 ĐS: (x+2)(3x-2)(5x+3) 132. a(b + c)(b2 – c2) + b(a + c)(a2 – c2) + c(a + b)(a2 – b2)
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