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Bài 1: 

a: \(x^3-6x^2+11x-6\)

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

\(=\left(x-1\right)\left(x^2-5x+6\right)\)

\(=\left(x-1\right)\left(x-2\right)\left(x-3\right)\)

b: \(x^3-6x^2-9x+14\)

\(=x^3-7x^2+x^2-7x-2x+14\)

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

\(=\left(x-7\right)\left(x+2\right)\left(x-1\right)\)

c: \(x^3+6x^2+11x+6\)

\(=x^3+3x^2+3x^2+9x+2x+6\)

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

\(=\left(x+3\right)\left(x+1\right)\left(x+2\right)\)

14 tháng 10 2020

a) x3 - 6x2 + 11x - 6

= ( x3 - 2x2 ) - ( 4x2 - 8x ) + ( 3x - 6 )

= x2( x - 2 ) - 4x( x - 2 ) + 3( x - 2 )

= ( x - 2 )( x2 - 4x + 3 )

= ( x - 2 )( x2 - x - 3x + 3 )

= ( x - 2 )[ x( x - 1 ) - 3( x - 1 ) ]

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

b) x3 - 6x2 - 9x + 14

= ( x3 - x2 ) - ( 5x2 - 5x ) - ( 14x - 14 )

= x2( x - 1 ) - 5x( x - 1 ) - 14( x - 1 )

= ( x - 1 )( x2 - 5x - 14 )

= ( x - 1 )( x2 + 2x - 7x - 14 )

= ( x - 1 )[ x( x + 2 ) - 7( x + 2 ) ]

= ( x - 1 )( x + 2 )( x - 7 )

c) x3 + 6x2 + 11x + 6

= ( x3 + 2x2 ) + ( 4x2 + 8x ) + ( 3x + 6 )

= x2( x + 2 ) + 4x( x + 2 ) + 3( x + 2 )

= ( x + 2 )( x2 + 4x + 3 )

= ( x + 2 )( x2 + x + 3x + 3 )

= ( x + 2 )[ x( x + 1 ) + 3( x + 1 ) ]

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

e) x6 - 9x3 + 8

Đặt t = x3

bthuc <=> t2 - 9t + 8 

            = t2 - t - 8t + 8

            = t( t - 1 ) - 8( t - 1 )

            = ( t - 1 )( t - 8 )

            = ( x3 - 1 )( x3 - 8 )

            = ( x - 1 )( x2 + x + 1 )( x - 2 )( x2 + 2x + 4 )

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

15 tháng 10 2016

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

                                       =\(\left[x^2+7x+10\right]\left[x^2+7x+12\right]\)

đặt \(x^2+7x+10=a\)

ta có \(a\left(a+2\right)-24=a^2+2a-24\)

                                      \(=a^2+2a+1-25\)

                                      \(=\left(a+1\right)^2-5^2\)

                                      \(=\left(a+1-5\right)\left(a+1+5\right)\)

                                     \(=\left(a-4\right)\left(a+6\right)\)

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

15 tháng 10 2016

a) = (x +5)2 - 22 = (x+5 -2)(x+5 +2) = (x+3)(x+7)

b) = x(x2 -1) -6(x-1)= x(x+1)(x-1) -6(x-1) = (x-1)(x(x+1)-6)

`@` `\text {Ans}`

`\downarrow`

`4x^3 - 4x^2 - 9x + 9`

`= (4x^3 - 4x^2) - (9x - 9)`

`= 4x^2(x - 1) - 9(x - 1)`

`= (4x^2 - 9)(x - 1)`

____

`x^3 + 6x^2 + 11x + 6`

`= x^3 + x^2 + 5x^2 + 5x + 6x + 6`

`= (x^3 + x^2) + (5x^2 + 5x) + (6x + 6)`

`= x^2*(x + 1) + 5x(x + 1) + 6(x + 1)`

`= (x^2 + 5x + 6)(x+1)`

____

`x^2y - x^3 - 9y + 9x`

`= (x^2y - 9y) - (x^3 - 9x)`

`= y(x^2 - 9) - x(x^2 - 9)`

`= (y - x)(x^2 - 9)`

b: =x^3+x^2+5x^2+5x+6x+6

=(x+1)(x^2+5x+6)

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

c: =x^2(y-x)-9(y-x)

=(y-x)(x^2-9)

=(y-x)(x-3)(x+3)

a: =(4x^3-4x^2)-(9x-9)

=4x^2(x-1)-9(x-1)

=(x-1)(4x^2-9)

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

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) \(x^3+5x^2-12\)

\(=\left(x^3+2x^2\right)+\left(3x^2+6x\right)-\left(6x+12\right)\)

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

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

14 tháng 8 2018

a)18x2-12x

=3x(6x-4)

b)3x2-11x+6

=x(3x-11+6)

=x(3x-5)

c)x3+6x2+11x+6

=x2(x+23

3 tháng 9 2018

\(18x^2-12x\)

\(=6x\left(3x-2\right)\)

\(3x^2-11x+6\)

\(=3x^2-9x-2x+6\)

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

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

25 tháng 10 2017

b, 2x2 + 3x - 27

=2x2+9x-6x-27

=x(2x+9)-3(2x+9)

=(x-3)(2x+9)

d, x3 - 7x + 6

=x3+0x2-7x+6

= x3-x2+x2-x-6x+6

= (x3-x2)+(x2-x)-(6x-6)

= x2(x-1)+x(x-1)-6(x-1)

= (x-1) (x2+x-6)

= (x-1)(x2-2x+3x-6)

=(x-1)[x(x-2)+3(x-2)]

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

20 tháng 10 2018

c) 2x\(^2\)- 5xy - 3y\(^2\)

= 2x\(^2\)- 6xy + xy - 3y\(^2\)

= 2x( x - 3y) + y( x - 3y)

= (2x + y)( x - 3y)

e) x3 + 5x2 + 8x + 4

= x3 + 2x2 + 3x2 + 6x + 2x + 4

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

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

Các câu còn lại cx làm tương tự theo cách này nha !!! Chúc bn học tốt