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

      = (3x + 1 + x + 1)(3x + 1 – x – 1)

      = (4x + 2).2x = 2( 2x + 1).2x

      = 4x(2x + 1)

#)Giải :

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

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

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

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

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

\(x^4+2x^3+5x^2+4x-12\)

\(=x^4+x^3+6x^2+x^3+x^2+6x-2x^2-2x-12\)

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

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

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

Câu 1.

Đoán được nghiệm là 2.Ta giải như sau:

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

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

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

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

cảm ơn nha!

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

\(x^3-x-12\)

\(=x^3-4x+3x-12\)

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

\(=x\left(x-4\right)\left(x+4\right)+3\left(x-4\right)\)

\(=\left(x-4\right)\left[x\left(x+4\right)+3\right]\)

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

x² - x - 12

= x² + 3x - 4x - 12

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

= (x - 4)(x + 3)

Trả lời:

x² - x - 12 

= x² - 4x + 3x - 12

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

= ( x + 3 ) ( x - 4 )

(x-4)*(x+3)

Phân tích đa thức thành nhân tử

\(x^2-x-12=x^2-x-9-3\)

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

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

\(=\left(x+3\right).\left(x-4\right)\)

\(x^2-x-12=x^2-3x+4x-12\)

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

\(=x\left(x-3\right)+4\left(x-3\right)\)

\(=\left(x-3\right)\left(x+4\right)\)

\(x^2-x-12=x^2-4x+3x-12\)

\(=x\left(x-4\right)+3\left(x-4\right)\)

\(=\left(x-4\right)\left(x+3\right)\)

\(4x\left(x-5\right)^2-12\left(4-x\right)^2\)

\(=4\left[x\left(x-5\right)^2-3\left(4-x\right)^2\right]\)

\(=4\left[x\left(x^2-10x+25\right)-3\left(16-8x+x^2\right)\right]\)

\(=4\left(x^3-10x^2+25x-48+24x-3x^2\right)\)

\(=4\left(x^3-13x^2+49x-48\right)\)

#Ayumu

\(x^2+2xy+y^2-x-y-12\)

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

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

\(=\left(x+y\right)\left(x+y-4\right)+3\left(x+y-4\right)\)

\(=\left(x+y-4\right)\left(x+y+3\right)\)