Bài tập phân tích đa thức thành nhân tử

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)