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

\(A=\left[\left(x-1\right)\left(x-4\right)\right]\left[\left(x-2\right)\left(x-3\right)\right]+1\)

\(A=\left(x^2-5x+4\right)\left(x^2-5x+6\right)+1\)

Đặt \(a=x^2-5x+5\)

\(\Leftrightarrow A=\left(a-1\right)\left(a+1\right)+1\)

\(\Leftrightarrow A=a^2-1^2+1\)

\(\Leftrightarrow A=a^2\)

Thay \(a=x^2-5x+5\)vào A ta có :

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

b) \(B=\left(x^2+3x+2\right)\left(x^2+7x+12\right)+1\)

\(B=\left(x^2+x+2x+2\right)\left(x^2+3x+4x+12\right)+1\)

\(B=\left[x\left(x+1\right)+2\left(x+1\right)\right]\left[x\left(x+3\right)+4\left(x+3\right)\right]+1\)

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

Làm tương tự câu a)

c) \(12x^2-3xy-8xz+2yz\)

\(=3x\left(4x-y\right)-2z\left(4x-y\right)\)

\(=\left(4x-y\right)\left(3x-2z\right)\)

a) \(\left(x^2-7x+12\right).\left(x^2-15x+56\right)-60\)

\(=\left(x-3\right)\left(x-4\right)\left(x-7\right)\left(x-8\right)-60\)

b) \(x^4+2000x^2+1999x+2000\)

\(=\left(x^2-x+2000\right)\left(x^2+x+1\right)\)

\(=\left(x^2+x-1\right)^2+1999\left(x^2+x+1\right)+1\)

hình như Thành lộn đề rồi đấy ạ, ý mình là phân tích thành nhân tử á

b) \(x^4+2000x^2+1999x+2000\)

\(=x^4-x+2000x^2+2000x+2000\)

\(=x\left(x^3-1\right)+2000\left(x^2+x+1\right)\)

\(=x\left(x-1\right)\left(x^2+x+1\right)+2000\left(x^2+x+1\right)\)

\(=\left(x^2+x+1\right)\left(x^2-x-2000\right)\)

a. \(x^2\) - 9y²

= (\(x\))² - (3y)²

= (\(x\) - 3y)(\(x\) + 3y)

x² - 9y² = x² - (3y)²= (x - 3y)(x + 3y)

B. 7\(x\).(\(x\) - y) + 3\(x\) - 3y

= 7\(x\).(\(x\) -y) + 3.(\(x\) - y)

= (\(x\) - y)(7\(x\) + 3)

Lời giải:
a.

$x^2-7x+6=(x^2-x)-(6x-6)=x(x-1)-6(x-1)=(x-1)(x-6)$

b.

$x-3\sqrt{3}x-12\sqrt{3}$ không phân tích được thành nhân tử

c.

$x^2+4x-2$ không phân tích được thành nhân tử với các hệ số nguyên.

\(a,=\left(x+1\right)\left(x+3\right)\\ b,=-5x^2+15x+x-3=\left(x-3\right)\left(1-5x\right)\\ c,=2x^2+2x+5x+5=\left(2x+5\right)\left(x+1\right)\\ d,=2x^2-2x+5x-5=\left(x-1\right)\left(2x+5\right)\\ e,=x^3+x^2-4x^2-4x+x+1=\left(x+1\right)\left(x^2-4x+1\right)\\ f,=x^2+x-5x-5=\left(x+1\right)\left(x-5\right)\)

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

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

\(C=3x^2+7x+4=\left(x+1\right)\left(3x+4\right)\)

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

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

\(C=3x^2+7x+4=\left(x+1\right)\left(3x+4\right)\)

A = x² + 3x + 2

A = x² + x + 2x + 2

A = x(x + 1) + 2(x + 1)

A = (x + 2)(x + 1)

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

\(a,=\left(x-2\right)^2-y^2=\left(x-y-2\right)\left(x+y-2\right)\\ b,=4x^2\left(x^2+2x+1\right)=4x^2\left(x+1\right)^2\\ c,=xy^2\left(x^2-2xy+y^2\right)=xy^2\left(x-y\right)^2\\ d,=\left(x-y\right)\left(x+y\right)-7\left(x-y\right)=\left(x-y\right)\left(x+y-7\right)\\ e,=\left(5x-2y\right)\left(5x+2y\right)\\ f,=x^2+3x+4x+12=\left(x+3\right)\left(x+4\right)\\ i,=x^2+2x-7x-14=\left(x+2\right)\left(x-7\right)\)

Phân tích đa thức thành nhân tử:

a) x² (2x - 5) + 6x - 15 =  x² (2x - 5) + 3(2x - 5) =( x2 + 3 )(2x - 5)

b)x² + 7x + 12 =  x² + 3x + 4x + 12 = (x + 3 )( x + 4)

\(a,A=x^2+7x+7y-y^2\\ =x^2-y^2+7x+7y\\ =\left(x-y\right)\left(x+y\right)+7\left(x+y\right)\\ =\left(x+y\right)\left(x-y+7\right)\)

\(b,B=x^2+2xy+y^2-3x-3y\\ =\left(x+y\right)^2-3\left(x+y\right)\\ =\left(x+y\right)\left(x+y-3\right)\)