\(x^2+7x+12=x\left(x+3\right)+4\left(x+3\right)=\left(x+3\right)\left(x+4\right)\)

\(=x^2+3x+4x+12\)
\(=x\left(x+3\right)+4\left(x+3\right)\)
\(=\left(x+3\right)\left(x+4\right)\)

\(4x^2-7x-2\\ =4x^2-8x+x-2\\ =4x\left(x-2\right)+\left(x-2\right)\\ =\left(x-2\right)\left(4x+1\right)\)

\(-2x^4-7x^3-x^2+7x+3\)

\(=-2x^3\left(x+1\right)-5x^2\left(x+1\right)+4x\left(x+1\right)+3\left(x+1\right)\)

\(=-\left(x+1\right)\left(2x^3+5x^2-4x-3\right)\)

\(=-\left(x+1\right)\left[2x^2\left(x-1\right)+7x\left(x-1\right)+3\left(x-1\right)\right]\)

\(=-\left(x+1\right)\left(x-1\right)\left(2x^2+7x+3\right)\)

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

x³ + 7x - 6

= x³ - x - 6x - 6

= x³ - x - 6 (x+1)

= x (x² - 1) - 6 (x+1)

= (x + 1) ( x (x - 1) - 6 )

= ( x + 1) ((x² - x - 6))

= (x + 1) ((x² + 2 - 3 - 6))

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

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

7x - 6x² - 2

= - ( 6x² - 7x + 2)

= - ( 6x² - 3x - 4x + 2 )

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

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

~ Học tốt ~

\(7x-6x^2-2\)

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

\(=-\left(6x^2-3x-4x+2\right)\)

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

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

\(7x-6x^2-2\)

\(=\left(3x-6x^2\right)-\left(2-4x\right)\)

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

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

(x^2 +7x)-(y^2+7y)

=x(x+7)-y(y+7)

=(x+7)(y+7)(x-y)

\(4x^2-49=\left(2x\right)^2-7^2=\left(2x-7\right)\left(2x+7\right)\)

cho mình hỏi dấu ^ có ngĩa là gì

`x^3 - 5x^2 + 8x + 4`

`= x^3 + x^2 + 4x^2 + 4x + 4x + 4`

`= x^2(x + 1) + 4x(x + 1) + 4(x + 1)`

`= (x + 1)(x^2 + 4x 4)`

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