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NV
3 tháng 1

a.

\(x^4+4=x^4+4x^2+4-4x^2\)

\(=\left(x^2+2\right)^2-\left(2x\right)^2=\left(x^2-2x+2\right)\left(x^2+2x+2\right)\)

b.

\(x^3-9x^2+6x+16=\left(x^3-7x^2-8x\right)-\left(2x^2-14x-16\right)\)

\(=x\left(x^2-7x-8\right)-2\left(x^2-7x-8\right)\)

\(=\left(x-2\right)\left(x^2-7x-8\right)=\left(x-2\right)\left(x^2+x-8x-8\right)\)

\(=\left(x-2\right)\left[x\left(x+1\right)-8\left(x+1\right)\right]=\left(x-2\right)\left(x+1\right)\left(x-8\right)\)

c.

\(\left(x+2\right)\left(x+3\right)\left(x+4\right)\left(x+5\right)-24\)

\(=\left(x+2\right)\left(x+5\right)\left(x+3\right)\left(x+4\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+10+2\right)-24\)

\(=\left(x^2+7x+10\right)^2+2\left(x^2+7x+10\right)-24\)

\(=\left(x^2+7x+10\right)^2-4\left(x^2+7x+10\right)+6\left(x^2+7x+10\right)-24\)

\(=\left(x^2+7x+10\right)\left(x^2+7x+10-4\right)+6\left(x^2+7x+10-4\right)\)

\(=\left(x^2+7x+10-4\right)\left(x^2+7x+10+6\right)=\left(x^2+7x+6\right)\left(x^2+7x+16\right)\)

\(=\left(x+1\right)\left(x+6\right)\left(x^2+7x+16\right)\)

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: \(\left(x^2-3\right)^2+16\)

\(=x^4-6x^2+9+16\)

\(=x^4-6x^2+25\)

\(=x^4+10x^2+25-16x^2\)

\(=\left(x^2+5\right)^2-\left(4x\right)^2\)

\(=\left(x^2+5+4x\right)\left(x^2+5-4x\right)\)

 

30 tháng 7 2018

a)   x3 -2x2 +5x-4

=x3-x2-x2+x+4x-4

=x2(x-1)-x(x-1)+4(x-1)

=(x2-x+4)(x-1)

b) x3-x2+x+3

=x3+x2-2x2-2x+3x+3

=x2(x+1) -2x(x+1)+3(x+1)

=(x2-2x+3)(x+1)

c) 6x3+x2+x+1

=6x3+ 3x2-2x2-x+2x+1

=6x2(x+\(\frac{1}{2}\)) - 2x(x+\(\frac{1}{2}\)) +2(x+\(\frac{1}{2}\))

=(6x2-2x+2) (x+\(\frac{1}{2}\))

=2( 3x2-x+1) (x+\(\frac{1}{2}\))

d)  4x3 + 6x2+4x+1

= 4x3+2x2+4x2+2x+2x+1

= 4x2(x+\(\frac{1}{2}\))+ 4x(x+\(\frac{1}{2}\))+2(x+\(\frac{1}{2}\))

= 2(2x2 +2x+1)( x+\(\frac{1}{2}\))

e) x6 -9x3+8

1 tháng 10 2018

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 )

26 tháng 7 2017

a) bt \(=\left(x-8\right)\left(x^2-x-2\right)=\left(x-8\right)\left(x+1\right)\left(x-2\right)\)

kl: ...

b) \(=\left(x+2\right)\left(x^2-8x-15\right)=\left(x+2\right)\left(x-5\right)\left(x-3\right)\)

kl:....

26 tháng 7 2017

a, \(x^3-9x^2+6x+16\)

\(=x^3-8x^2-x^2+8x-2x+16\)

\(=x^2\left(x-8\right)-x\left(x-8\right)-2\left(x-8\right)\)

\(=\left(x-8\right)\left(x^2-x-2\right)\)

\(=\left(x-8\right)\left(x^2-2x+x-2\right)\)

\(=\left(x-8\right)\left[x\left(x-2\right)+\left(x-2\right)\right]\)

\(=\left(x-8\right)\left(x-2\right)\left(x+1\right)\)

b, \(x^3-6x^2-x+30\)

\(=x^3-5x^2-x^2+5x-6x+30\)

\(=x^2\left(x-5\right)-x\left(x-5\right)-6\left(x-5\right)\)

\(=\left(x-5\right)\left(x^2-x-6\right)\)

\(=\left(x-5\right)\left(x^2-3x+2x-6\right)\)

\(=\left(x-5\right)\left[x\left(x-3\right)+2\left(x-3\right)\right]\)

\(=\left(x-5\right)\left(x-3\right)\left(x+2\right)\)

Chúc bạn học tốt!!!

15 tháng 8 2021

Đề bạn có mấy chỗ thiếu mk bổ sung nha

\(a,2^3+4^2+6x=8+16+6x=6x+24=x\left(x+4\right)\\ b,x^2-4=\left(x-2\right)\left(x+2\right)\\ c,x^2-10x+25=\left(x-5\right)^2\\ d,x^3-4x=x\left(x^2-4\right)=x\left(x-2\right)\left(x+2\right)\\ e,x^2+xy-3x-3y=x\left(x+y\right)-3\left(x+y\right)=\left(x-3\right)\left(x+y\right)\\ g,x^2-y^2-4x+4=\left(x-2\right)^2-y^2=\left(x-y-2\right)\left(x+y-2\right)\)

Tick plzz

 

a: Ta có: \(2x^3+4x^2+6x\)

\(=2x\left(x^2+2x+3\right)\)

b: \(x^2-4=\left(x-2\right)\left(x+2\right)\)

c: \(x^2-10x+25=\left(x-5\right)^2\)

d: \(x^3-4x=x\left(x-2\right)\left(x+2\right)\)

e: \(x^2+xy-3x-3y\)

\(=x\left(x+y\right)-3\left(x+y\right)\)

\(=\left(x+y\right)\left(x-3\right)\)

g: \(x^2-4x+4-y^2\)

\(=\left(x-2\right)^2-y^2\)

\(=\left(x-y-2\right)\left(x+y-2\right)\)

5 tháng 1 2021

1. 1582 - 116.158 + 582

= 1582 - 2.58.158 + 582

= (158 - 58)2

= 1002 = 10000

2.a. 8x2 + 6x = 2x(4x + 3)

b, x3 - 5x2 - 4x + 20

= x3 - 4x - 5x2 + 20

= x(x2 - 4) - 5(x2 - 4)

= (x - 5)(x - 2)(x + 2)

6 tháng 7 2016

câu này gửi rồi mà tôi lm rồi đó Câu hỏi của nguyen thi diem quynh - Toán lớp 8 - Học toán với OnlineMath

6 tháng 7 2016

a. 1+6x-6x2-x3
=(1-x3)+(6x-6x2
=(1-x)(1+x+x2)+6x(1-x) 
=(1-x)(1+x+x2+6x) 
=(1-x)(1+7x+x2

b. x3-2x-4 
=x3-4x+2x-4 
=x(x2-4)+2(x-2) 
=x(x-2)(x+2)+2(x-2) 
=(x2+2x+2)(x-2) 
 Ủng hộ mk nhak ^_-