Bµi tËp ph©n tÝch ®a thøc thµnh nh©n tö 1. 16x 3 y + 0,25yz 3 §S: 1/4y(4x + z)(16x 2 - 4xz + z 2 ) 59. (a + b + c) 2 + (a + b – c) 2 – 4c 2 §S: 2(a+b+c)(a+b-c) 2. x 4 – 4x 3 + 4x 2 §S: x 2 (x - 2) 2 60. 4a 2 b 2 – (a 2 + b 2 – c 2 ) 2 §S: (a+b-c)(a+b+c) (c+a-b)(c-a+b) 3. 2ab 2 – a 2 b – b 3 §S: - b(a- b) 2 61. a 4 + b 4 + c 4 – 2a 2 b 2 – 2b 2 c 2 – 2a 2 c 2 §S: (a+b+c) (a-b-c) (a+b-c) (a-b+c) 4. a 3 + a 2 b – ab 2 – b 3 §S: (a-b)(a+b) 2 62. a(b 3 – c 3 ) + b(c 3 – a 3 ) + c(a 3 – b 3 ) §S: 5. x 3 + x 2 – 4x – 4 §S: (x+1)(x+2)(x-2) 63. a 6 – a 4 + 2a 3 + 2a 2 §S: a 2 (a+1) 2 (a 2 -2a+2) 6. x 3 – x 2 – x + 1 §S: (x-1) 2 (x+1) 64. (a + b) 3 – (a – b) 3 §S: 2b(3a 2 +b 2 ) 7. x 4 + x 3 + x 2 – 1 §S: (x+1)(x 3 +x-1) 65. x 3 – 3x 2 + 3x – 1 – y 3 §S: (x-y-1)(x 2 -2x+1+xy-y+y 2 ) 8. x 2 y 2 + 1 – x 2 – y 2 §S: (x+1)(x-1)(y+1)(y-1) 66. x m + 4 + x m + 3 – x – 1 §S: (x+1)(x m+3 -1) 10. x 4 – x 2 + 2x – 1 §S : (x 2 -x+1)(x 2 +x+1) 67. (x + y) 3 – x 3 – y 3 §S: 3xy(x+y) 11. 3a – 3b + a 2 – 2ab + b 2 (a-b)(3+a-b) 68. (x + y + z) 3 – x 3 – y 3 – z 3 §S: 3(x+y)(y+z)(z+x) 12. a 2 + 2ab + b 2 – 2a – 2b + 1 §S: (a+b-1) 2 69. (b – c) 3 + (c – a) 3 + (a – b) 3 §S: 3(a-b)(b-c)(c-a) 13. a 2 – b 2 – 4a + 4b §S: (a-b)(a+b-4) 70. x 3 + y 3 + z 3 – 3xyz §S: (x+y+z)(x 2 +y 2 +z 2 -xy-yz-zx) 14. a 3 – b 3 – 3a + 3b §S: (a-b)(a 2 +ab+b 2 -3) 71. (x + y) 5 – x 5 – y 5 §S: 5xy(x+y)(x 2 +3xy+y 2 ) 15. x 3 + 3x 2 – 3x – 1 §S: (x-1)(x 2 +4x+1) 72. (x 2 + y 2 ) 3 + (z 2 – x 2 ) 3 – (y 2 + z 2 ) 3 §S: 3(x 2 +y 2 )(y 2 +z 2 )(x-z)(x+z) 16. x 3 – 3x 2 – 3x + 1 §S: (x+1)(x 2 - 4x+1) 73 ab(a + b) + bc(b + c) + ca(c + a) + abc §S: 17. x 3 – 4x 2 + 4x – 1 §S: (x-1)(x 2 - 3x+1) 74 (x + y + z) 5 – x 5 – y 5 – z 5 §S: 5(x+y)(y+z)(z+x)(x 2 +y 2 +z 2 +xy+yz+zx) 18. 4a 2 b 2 – (a 2 + b 2 – 1) 2 §S: (1-a+b)(1+a-b)(a+b-1)(a+b+1) 75 a(b 2 + c 2 ) + b(c 2 + a 2 ) + c(a 2 + b 2 ) + 2abc §S: (a+b)(b+c)(c+a) 19. (xy + 4) 2 – (2x + 2y) 2 §S: (x+2)(x-2)(y+2)(y-2) 76 a 3 (b – c) + b 3 (c – a) + c 3 (a – b) §S: (a-b)(a-c)(b-c)(a+b+c) 20. (a 2 + b 2 + ab) 2 – a 2 b 2 – b 2 c 2 – c 2 a 2 §S:(a 2 +b 2 )(a+b+c)(a+b-c) 77 abc – (ab + bc + ac) + (a + b + c) – 1 §S: (a-1)(b-1)(c-1) 21. x 2 – 6x + 8 §S(B21):(x-2)(x-4) 78. x 3 – 5x 2 y – 14xy 2 §S(B78): x(x+2y)(x-7y) 1 22 x 2 – 7xy + 10y 2 §S: (x-2y)(x-5y) 79. x 4 – 7x 2 + 1 §S: (x 2 -3x+1)(x 2 +3x+1) 23 a 2 – 5a – 14 §S: (a-7)(a+2) 80. 4x 4 – 13x 2 + 1 §S: (x-2y)( 24 2m 2 + 10m + 8 §S: 2(m+1)(m+4) 81. x 2 + 8x + 7 §S: (x+7)(x+1) 25 4p 2 – 36p + 56 §S: 4(p-7)(p-2) 82. x 2 – 13x + 36 §S: (x-4)(x-9) 26 x 3 – 5x 2 – 14x §S: x(x-7)(x+2) 83. x 2 + 3x – 18 §S: (x+6)(x-3) 27 a 4 + a 2 + 1 §S: (a 2 +a+1)(a 2 - a+1) 84. x 2 – 5x – 24 §S: (x-8)(x+3) 28 a 4 + a 2 – 2 §S: (a-1)(a+1)(a 2 +2) 85. 3x 2 – 16x + 5 §S: (x-5)(3x-1) 29 x 4 + 4x 2 + 3 §S: (x 2 +1)(x 2 +3) 86. 8x 2 + 30x + 7 §S: (2x+7)(4x+1) 30. x 3 – 10x – 12 §S: (x+2)(x 2 -2x-6) 87. 2x 2 – 5x – 12 §S: (x-4)(2x+3) 31. x 3 – 7x – 6 §S: (x+1)(x+2)(x-3) 88. 6x 2 – 7x – 20 §S : (3x+4)(2x-5) 32. x 2 – 7x + 12 §S: (x-3)(x-4) 89. x 2 – 7x + 10 §S: (x-2)(x-5) 33. x 2 – 5x – 14 §S: (x+2)(x-7) 90. x 2 – 10x + 16 §S: (x-2)(x-8) 34. 4 x 2 – 3x – 1 §S: (x-1)(4x+1) 91. 3x 2 – 14x + 11 §S: (x-1)(3x-11) 35. 3 x 2 – 7x + 4 §S: (x-1)(3x-4) 92. 5x 2 + 8x – 13 §S: (x-1)(5x+13) 36. 2 x 2 – 7x + 3 §S: (2x-1)(x-3) 93. x 2 + 19x + 60 §S: (x+4)(x+15) 37. 6x 3 – 17x 2 + 14x – 3 §S: (x-1)(3x-1)(2x-3) 94. x 4 + 4x 2 – 5 §S: (x-1)(x+1)(x 2 -5) 38. 4x 3 – 25x 2 – 53x – 24 §S: (x+1)(x-8)(4x+3) 95. x 3 – 19x + 30 §S: (x-2)(x-3)(x+5) 39. x 4 – 34x 2 + 225 §S: (x+3)(x-3)(x+5)(x-5) 96. x 3 + 9x 2 + 26x + 24 §S: (x+3)(x+2)(x+4) 40. 4x 4 – 37x 2 + 9 §S: ((x+3)(x-3)(2x+1)(2x-1) 97. 4x 2 – 17xy + 13y 2 §S: (x-y)(4x-13y) 41. x 4 + 3x 3 + x 2 – 12x – 20 §S: (x-2)(x+2)(x 2 +3x+5) 98. - 7x 2 + 5xy + 12y 2 §S: (x+y)(12y-7x) 42. 2x 4 + 5x 3 + 13x 2 + 25x + 15 §S:(B42) (x+1)(2x 3 +3x 2 +10x+15) 99. x 3 + 4x 2 – 31x - 70 §S:(B99): (x+2)(x-5)(x+7) 2 43 x 4 + x 2 + 1 §S: (x 2 -x+1)(x 2 +x+1) 100. x 5 - x 4 – 1 §S: (x 3 -x-1)(x 2 -x+1) 44 x 4 – 3x 2 + 9 §S: ( 101 x 12 – 3x 6 + 1 §S: (x 6 +x 3 -1)(x 6 -x 3 -1) 45 x 4 + 3x 2 + 4 §S: (: (x 2 -x+2)(x 2 +x+2) 102 x 8 - 3x 4 + 1 §S: (x 4 -x 2 -1)(x 4 +x 2 -1) 46 2x 4 – x 2 – 1 §S: (x+1)(x-1)(2x 2 +1) 103 a 5 + a 4 + a 3 + a 2 + a + 1 §S: (a 2 -a+1) (a 2 +a+1)(a+1) 47 x 4 y 4 + 4 §S: (x 2 y 2 +2xy+2) (x 2 y 2 - 2xy+2) 104 m 3 – 6m 2 + 11m – 6 §S: (m-1)(m-2)(m-3) 48 x 4 y 4 + 64 §S: (x 2 y 2 +4xy+8) (x 2 y 2 -4xy+8) 105 x 4 + 6x 3 + 7x 2 – 6x + 1 §S: (x 2 +3x-1) 2 49 4 x 4 y 4 + 1 §S: (2x 2 y 2 -2xy+1) (2x 2 y 2 +2xy+1) 106 x 3 + 4x 2 – 29x + 24 §S: (x-1)(x-8)(x+3) 50 32x 4 + 1 §S: ( 107 x 10 + x 8 + x 6 + x 4 + x 2 + 1 §S:( x 2 +1) (x 4 -x 2 +1) (x 2 -x+1) (x 2 +x+1) 51 x 4 + 4y 4 §S: (x 2 - 2xy+2y 2 ) (x 2 + 2xy+2y 2 ) 108 x 7 + x 5 + x 4 + x 3 + x 2 + 1 §S: (x+1)(x 6 - x 5 +2 x 4 -x 3 +2x 2 -x+1) 52. x 7 + x 2 + 1 §S: (x 2 +x+1)(x 5 -x 4 +x 2 -x+1) 109 x 5 – x 4 – x 3 – x 2 – x – 2 §S: ( 53. x 8 + x + 1 §S:( x 2 +x+1)(x 6 -x 5 +x 3 -x 2 +1) 110 x 8 + x 6 + x 4 + x 2 + 1 §S: ( 54. x 8 + x 7 + 1 §S: (x 2 +x+1)(x 6 -x 4 +x 3 -x+1) 111 x 9 – x 7 – x 6 – x 5 + x 4 + x 3 + x 2 + 1 §S: ( 55. x 8 + 3x 4 + 1 §S: ( 112 a(b 3 – c 3 ) + b(c 3 – a 3 ) + c(a 3 – b 3 ) §S: (a-b)(b-c)(c-a)(a+b+c) 56. x 10 + x 5 + 1 §S: (x 2 +x+1)(x 8 -x 7 +x 5 - x 4 +x 3 - x+1) 113 4(x 2 + 15x + 50)(x 2 + 18x + 72) – 3x 2 §S: ( 57. x 5 + x + 1 §S: (x 2 +x+1)(x 3 -x 2 +1) 114 (x 2 + x) 2 + 4(x 2 + x) – 12 §S: ( 58. x 5 + x 4 + 1 §S : (x 2 +x+1)(x 3 -x+1) 115 (x + y) 7 – x 7 – y 7 116. x 2 + 2xy – 8y 2 + 2xz + 14yz – 3z 2 133. (x + 2)(x + 4)(x + 6)(x + 8) + 16 §S: (x+4y-z)(x-2y+3z) §S: (x 2 +x+20) 2 117. 3x 2 – 22xy – 4x + 8y + 7y 2 + 1 134. x 4 – 6x 3 + 7x 2 + 6x – 8 §S: (3x-y-1)(x-7y-1) §S: (x-1) (x-2) (x+1) (x-4) 118. 12x 2 + 5x – 12y 2 + 12y – 10xy – 3 135. x 3 + 9x 2 + 26x + 24 §S: (3x+2y-1)(4x-6y+3) §S: (x+2) (x+3) (x+4) 119. 2x 2 – 7xy + 3y 2 + 5xz – 5yz + 2z 2 136. ab(a – b) + bc(b – c) + ca(c – a) §S: (x-3y+2z)(2x-y+z) §S: (a-b)(b-c)(a-c) 120. x 2 + 3xy + 2y 2 + 3xz + 5yz + 2z 2 137. a(b 2 – c 2 ) – b(a 2 – c 2 ) + c(a 2 – b 2 ) §S:(B120) (x+2y+z)(x+y+2z) §S(B137): b(a-c)(b-a-c) 3 121. x 2 – 8xy + 15y 2 + 2x – 4y – 3 138. (x – y) 5 + (y – z) 5 + (z – x) 5 §S: (3x-y-1)(x-5y+3) §S: 122. x 4 – 13x 2 + 36 139. (x 2 + x) 2 + 4x 2 + 4x – 12 (bá) §S: (x-2)(x+2)(x-3)(x+3) §S: (x 2 +x-2) (x 2 +x+6) 123. x 4 + 3x 2 – 2x + 3 140. (x 2 + 4x + 8) 2 + 3x(x 2 + 4x + 8) + 2x 2 §S: (x 2 +x+3) (x 2 -x+1) §S: (x 2 +5x+8)(x+2)(x+4) 124. x 4 + 2x 3 + 3x 2 + 2x + 1 141. (x + 1)(x + 2)(x + 3)(x + 4) – 24 §S: §S: x(x+5)(x 2 +5x+10) 125. (a – b) 3 + (b – c) 3 + (c – a) 3 (bá) 142. (x 2 + 2x) 2 + 9x 2 + 18x + 20 §S: 3(a-b)(b-c)(c-a) §S: (x 2 +2x+4) (x 2 +2x+5) 126. (a – x)y 3 – (a – y)x 3 – (x – y)a 3 143. x 2 – 4xy + 4y 2 – 2x + 4y – 35 §S: §S: (x-2y+5)(x-2y-7) 127. x(y 2 – z 2 ) + y(z 2 – x 2 ) + z(x 2 – y 2 ) §S: (x-y)(y-z)(z-x) 129. 3x 5 – 10x 4 – 8x 3 – 3x 2 + 10x + 8 §S: (x-1)( )( ) 130. 5x 4 + 24x 3 – 15x 2 – 118x + 24 §S: (x-2)(5x 3 +34x 2 +53x-12) 131. 15x 3 + 29x 2 – 8x – 12 §S: (x+2)(3x-2)(5x+3) 132. a(b + c)(b 2 – c 2 ) + b(a + c)(a 2 – c 2 ) + c(a + b)(a 2 – b 2 ) 4