Bài tập : Phân tích đa thức thành nhân tử
a, x^3-7x+6
b, x^3-9x^2+6x+16
c, x^3-6x^2-x+30
d, 2x^3-x^2+5x+3
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1 tháng 2
a: \(x^3-9x^2+6x+16\)
\(=x^3-8x^2-x^2+8x-2x+16\)
\(=x^2\left(x-8\right)-x\left(x-8\right)-2\left(x-8\right)\)
\(=\left(x-8\right)\left(x^2-x-2\right)\)
\(=\left(x-8\right)\left(x-2\right)\left(x+1\right)\)
b: \(x^3-x^2-x-2\)
\(=x^3-2x^2+x^2-2x+x-2\)
\(=x^2\left(x-2\right)+x\left(x-2\right)+\left(x-2\right)\)
\(=\left(x-2\right)\cdot\left(x^2+x+1\right)\)
c: \(x^3+x^2-x+2\)
\(=x^3+2x^2-x^2-2x+x+2\)
\(=x^2\left(x+2\right)-x\left(x+2\right)+\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-x+1\right)\)
d: \(x^3-6x^2-x+30\)
\(=x^3+2x^2-8x^2-16x+15x+30\)
\(=x^2\left(x+2\right)-8x\left(x+2\right)+15\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2-8x+15\right)\)
\(=\left(x+2\right)\left(x-3\right)\left(x-5\right)\)
e: Sửa đề: \(x^3-7x-6\)
\(=x^3-x-6x-6\)
\(=x\left(x^2-1\right)-6\left(x+1\right)\)
\(=x\left(x-1\right)\left(x+1\right)-6\left(x+1\right)\)
\(=\left(x+1\right)\left(x^2-x-6\right)\)
\(=\left(x+1\right)\left(x-3\right)\left(x+2\right)\)
f: \(27x^3-27x^2+18x-4\)
\(=27x^3-9x^2-18x^2+6x+12x-4\)
\(=9x^2\left(3x-1\right)-6x\left(3x-1\right)+4\left(3x-1\right)\)
\(=\left(3x-1\right)\left(9x^2-6x+4\right)\)
g: \(2x^3-x^2+5x+3\)
\(=2x^3+x^2-2x^2-x+6x+3\)
\(=x^2\left(2x+1\right)-x\left(2x+1\right)+3\left(2x+1\right)\)
\(=\left(2x+1\right)\left(x^2-x+3\right)\)
h: \(\left(x^2-3\right)^2+16\)
\(=x^4-6x^2+9+16\)
\(=x^4-6x^2+25\)
\(=x^4+10x^2+25-16x^2\)
\(=\left(x^2+5\right)^2-\left(4x\right)^2\)
\(=\left(x^2+5+4x\right)\left(x^2+5-4x\right)\)
BM
1
8 tháng 10 2019
6x3 + 5x2 - 7x - 4
= (6x3 + 5x - 7x) - 4
= x (6x2 - 5 - 7) - 22
= x (6x2 - 12) - 22
= x [6 (x2 - 2)] - 22
= x [6 (x2 - \(\sqrt{2}^2\))] - 22
= x [6 (x +\(\sqrt{2}\)) (x -\(\sqrt{2}\))] - 22
= (x - 22) [6 (x +\(\sqrt{2}\)) (x -\(\sqrt{2}\))
b) 2x3 - x2 + x - 2
= (2x3 - x2 - x) - 2
= x (2x2 - x - 1) - 2
= (x - 2) (2x2 - x - 1)
(mik ko biet dug ko, neu sai mog bn thog cam)
1 tháng 10 2020
1) \(x^3+2x-3\)
\(=\left(x^3-x^2\right)+\left(x^2-x\right)+\left(3x-3\right)\)
\(=x^2\left(x-1\right)+x\left(x-1\right)+3\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2+x+3\right)\)
2) \(x^3-6x+4\)
\(=\left(x^3-2x^2\right)+\left(2x^2-4x\right)-\left(2x-4\right)\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)-2\left(x-2\right)\)
\(=\left(x-2\right)\left(x^2+2x-2\right)\)
1 tháng 10 2020
3) \(x^3-2x^2+1\)
\(=\left(x^3-x^2\right)-\left(x^2-x\right)-\left(x-1\right)\)
\(=x^2\left(x-1\right)-x\left(x-1\right)-\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-x-1\right)\)
4) \(x^3+5x^2-12\)
\(=\left(x^3+2x^2\right)+\left(3x^2+6x\right)-\left(6x+12\right)\)
\(=x^2\left(x+2\right)+3x\left(x+2\right)-6\left(x+2\right)\)
\(=\left(x+2\right)\left(x^2+3x-6\right)\)
26 tháng 6 2023
2: =(2x+1)^2-y^2
=(2x+1+y)(2x+1-y)
3: =x^2(x^2+2x+1)
=x^2(x+1)^2
4: =x^2+6x-x-6
=(x+6)(x-1)
5: =-6x^2+3x+4x-2
=-3x(2x-1)+2(2x-1)
=(2x-1)(-3x+2)
6: =5x(x+y)-(x+y)
=(x+y)(5x-1)
7: =2x^2+5x-2x-5
=(2x+5)(x-1)
8: =(x^2-1)*(x^2-4)
=(x-1)(x+1)(x-2)(x+2)
9: =x^2(x-5)-9(x-5)
=(x-5)(x-3)(x+3)
3 tháng 10 2021
\(a,=x^2-6x-x+6=\left(x-6\right)\left(x-1\right)\\ b,=x\left(x^2-4x+4\right)=x\left(x-2\right)^2\\ c,=x^3-x^2+2x^2-2x+2x-2=\left(x-1\right)\left(x^2+2x+2\right)\\ d,=x^2+2x+3x+6=\left(x+2\right)\left(x+3\right)\\ e,=x^2\left(x-6\right)+\left(x-6\right)=\left(x^2+1\right)\left(x-6\right)\\ f,=x^3\left(x^2+1\right)+\left(x^2+1\right)=\left(x^3+1\right)\left(x^2+1\right)\\ =\left(x+1\right)\left(x^2-x+1\right)\left(x^2+1\right)\)
KT
23 tháng 7 2018
a) \(x^3-2x^2+5x-4\)
\(=x^3-x^2-x^2+x+4x-4\)
\(=x^2\left(x-1\right)-x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(x^2-x+4\right)\)
b) \(x^3-x^2+x+3=\left(x+1\right)\left(x^2-2x+3\right)\)
c) \(x^3-6x^2-9x+14=\left(x-7\right)\left(x-1\right)\left(x+2\right)\)
d) \(x^4+2x^2-3=\left(x-1\right)\left(x+1\right)\left(x^2+3\right)\)
H9
HT.Phong (9A5)
CTVHS
22 tháng 10 2023
a) \(x^3+4x^2-21x\)
\(=x\left(x^2+4x-21\right)\)
\(=x\left(x^2-3x+7x-21\right)\)
\(=x\left[x\left(x-3\right)+7\left(x-3\right)\right]\)
\(=x\left(x-3\right)\left(x+7\right)\)
b) \(5x^3+6x^2+x\)
\(=x\left(5x^2+6x+1\right)\)
\(=x\left(5x^2+5x+x+1\right)\)
\(=x\left[5x\left(x+1\right)+\left(x+1\right)\right]\)
\(=x\left(x+1\right)\left(5x+1\right)\)
c) \(x^3-7x+6\)
\(=x^3+2x^2-3x-2x^2-4x+6\)
\(=x\left(x^2+2x-3\right)-2\left(x^2+2x-3\right)\)
\(=\left(x-2\right)\left(x^2+2x-3\right)\)
\(=\left(x-2\right)\left(x-1\right)\left(x+3\right)\)
d) \(3x^3+2x-5\)
\(=3x^3+3x^2+5x-3x^2-3x-5\)
\(=x\left(3x^2+3x+5\right)-\left(3x^2+3x+5\right)\)
\(=\left(x-1\right)\left(3x^2+3x+5\right)\)
29 tháng 9 2016
a, x^2 + 5x +4
= x^2 + 1x + 4x + 4
= (x^2 + 1x) + (4x + 4)
= x ( x + 1 ) + 4 ( x + 1 )
= (x + 1) (x + 4)
b, x^2 - 6x + 5
= x^2 - 1x - 5x + 5
= (x^2 - 1x) - (5x - 5)
= x (x - 1) - 5 (x - 1)
= (x - 1) (x - 5)
c, x^2 + 7x + 12
= x^2 + 3x + 4x + 12
= (x^2 + 3x) + (4x + 12)
= x (x + 3) + 4 (x + 3)
= (x + 3) (x + 4)
d, 2x^2 - 5x + 3
= 2^x2 - 2x - 3x + 3
= 2x (x - 1) - 3 (x - 1)
= (x-1) (2x - 3)
e, 7x - 3x^2 - 4
= 3x + 4x - 3x^2 - 4
= (3x - 3x^2) + (4x - 4)
= 3x (1 - x) + 4 (x - 1)
= 3x (1-x) - 4 (1 - x)
= (1 - x) (3x - 4)
f, x^2 - 10x + 16
= x^2 - 2x - 8x + 16
= (x^2 - 2x) - (8x - 16)
= x (x - 2) - 8 (x - 2)
= (x - 2) (x - 8)
VD
29 tháng 9 2016
a, (x+1)(x+4)
b,(x-5)(x-1)
c,(x+3)(x+4)
d,(2x-3)(x-1)
e,(-3x+4)(x-1)
f, (x-8)(x-2)
a) x3 - 7x + 6
= x3 - 2x2 + 2x2 - 4x - 3x + 6
= x2 ( x - 2 ) + 2x ( x - 2 ) - 3 ( x - 2 )
= ( x - 2 ) ( x2 + 2x - 3 )
= ( x - 2 ) ( x2 - x + 3x - 3 )
= ( x - 2 ) [ x ( x - 1 ) + 3 ( x - 1 ) ]
= ( x - 2 ) ( x - 1 ) ( x + 3 )
b ) x3 - 9x2 + 6x + 16
= x3 - 8x2 - x2 + 8x - 2x + 16
= x2 ( x - 8 ) - x ( x - 8 ) - 2 ( x - 8 )
= ( x - 8 ) ( x2 - x - 2 )
= ( x - 8 ) ( x2 + x - 2x - 2 )
= ( x - 8 ) [ x ( x + 1 ) - 2 ( x + 1 ) ]
= ( x - 8 ) ( x + 1 ) ( x - 2 )
c ) x3 - 6x2 - x + 30
= x3 - 5x2 - x2 + 5x - 6x + 30
= x2 ( x - 5 ) - x ( x - 5 ) - 6 ( x - 5 )
= ( x - 5 ) ( x2 - x - 6 )
= ( x - 5 ) ( x2 - 3x + 2x - 6 )
= ( x - 5 ) [ x ( x - 3 ) + 2 ( x - 3 ) ]
= ( x - 5 ) ( x - 3 ) ( x + 2 )
d ) 2x3 - x2 + 5x + 3
= 2x3 + x2 - 2x2 - x + 6x + 3
= x2 ( 2x + 1 ) - x ( 2x + 1 ) + 3 ( 2x + 1 )
= ( 2x + 1 ) ( x2 - x + 3 )