\(3x^4+11x^3-7x^2-2x+1=\left(3x^4+12x^3-3x^2-3x\right)+\left(-x^3-4x^2+x+1\right)\)

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

lấy máy tính bấm nghiệm ra

\(=2\left[\left(x-3\right)^2-\dfrac{1}{16}\left(x-1\right)^2\right]\\ =2\left(x-3-\dfrac{1}{4}x+\dfrac{1}{4}\right)\left(x-3+\dfrac{1}{4}x-\dfrac{1}{4}\right)\\ =2\left(\dfrac{3}{4}x-\dfrac{11}{4}\right)\left(\dfrac{5}{4}x-\dfrac{13}{4}\right)\)

`#040911`

`a)`

`x^2 + y^2 + 2xy - 25`

`= (x^2 + 2xy + y^2) - 25`

`= [ (x)^2 + 2*x*y + (y)^2] - 5^2`

`= (x + y)^2 - 5^2`

`= (x + y - 5)(x + y + 5)`

`b)`

`x^2 + 2x - 15`

`= x^2 + 5x - 3x - 15`

`= (x^2 + 5x) - (3x + 15)`

`= x(x + 5) - 3(x + 5)`

`= (x - 3)(x + 5)`

`c)`

`x^2 - x - 2`

`= x^2 - 2x + x - 2`

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

`= x(x - 2) + (x - 2)`

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

`d)`

`3x^2 - 11x + 6`

`= 3x^2 - 9x - 2x + 6`

`= (3x^2 - 9x) - (2x - 6)`

`= 3x(x - 3) - 2(x - 3)`

`= (3x - 2)(x - 3)`

`a, (x+y)^2-25 = (x+y+5)(x+y-5)`.

`b, x^2+2x-15 = (x+1)^2-16 = (x-3)(x+5)`.

`c, x^2-x-2=(x-2)(x+1)`

`d, 3x^2-11x+6 = (3x-2)(x-3)`.

\(a)x^2+y^2+2xy-25\\ =\left(x+y\right)^2-5^2\\ =\left(x+y+5\right)\left(x+y-5\right)\\ b)x^2+2x-15\\ =x^2+2x+1-16\\ =\left(x+1\right)^2-4^2\\ =\left(x+1+4\right)\left(x+1-4\right)\\ =\left(x+5\right)\left(x-3\right)\\ c)x^2-x-2\\ x^2+x-2x-2\\ =x\left(x+1\right)-2\left(x+1\right)\\ =\left(x+1\right)\left(x-2\right)\\ d)3x^2-11x+6\\ =3x^2-2x-9x+6\\ =x\left(3x-2\right)-3\left(3x-2\right)\\ =\left(x-3\right)\left(3x-2\right)\)

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

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

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

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

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

3x² - 11x + 6 

= 3x² - 2x - 9x + 6

= ( 3x² - 2x ) - ( 9x - 6 )

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

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

Bài làm

\(3x^2-11x+6=\left(3x-2\right)\left(x-3\right)\)

\(a,3x^2-11x+6=3x^2-9x-2x+6=3x\left(x-3\right)-2\left(x-3\right)=\left(3x-2\right)\left(x-3\right)\)

\(b,8x^2+10x-3=8x^2+12x-2x-3=4x\left(2x+3\right)-\left(2x+3\right)=\left(4x-1\right)\left(2x+3\right)\)

\(c,8x^2-2x-1=9x^2-x^2-2x-1=9x^2-\left(x+1\right)^2=\left(3x-x-1\right)\left(3x+x+1\right)\)

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

b, x³+x²-4x²-4x+4x+4

Sau đó phân tích tiếp

= 3x^2 - 2x-9x+6

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

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

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