\(x^6+2x^5+x^4-2x^3-2x^2+1=\left(x^3+x^2-1\right)^2\)

A = (x² - 2x)(x² - 2x - 1) - 6

= x⁴ - 4x³ + 3x² + 2x - 6 

= (x⁴ - 3x³) + (- x³ + 3x²) + (2x - 6)

= (x - 3)(x³ - x² + 2)

= (x - 3)[(x³ + x²) + ( - 2x² + 2)]

= (x - 3)(x + 1)(x² - 2x + 2)

x^40+2.x^20+9 = [x^20 +3]^2 - 4x^20 = [x^20+3]^2 -[2x^10]^2 = [x^20-2x^10+3].[x^20+2x^10+3]

x^12+x^6+1 = x^12 + 2x^6 +1 - x^6 = [x^6 +1]^2 -[x^3]^2 = [x^6 -x^3 +1].[x^6+x^3+1]

x^16+x^8+1 =[x^8+1]^2 - [x^4]^2 = [x^8-x^4+1].[x^8+x^4+1]

x^4+x^2+1 = x^4+2x^2+1 - x^2 = [x^2+1]^2-x^2 = [x^2-x+1].[x^2+x+1]

Bài 1: 

a) \(x^3-16x=x\left(x-4\right)\left(x+4\right)\)

b) \(3x^2+3y^2-6xy-12=3\left(x^2-2xy+y^2-4\right)=3\left(x-y-2\right)\left(x-y+2\right)\)

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

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

Bài 2: 

a) Ta có: \(\left(x+6\right)^2=144\)

\(\Leftrightarrow\left[{}\begin{matrix}x+6=12\\x+6=-12\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-18\end{matrix}\right.\)

b) Ta có: \(x^3+27+\left(x+3\right)\left(x-9\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)

\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\)

\(\Leftrightarrow x\left(x+3\right)\left(x-2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-3\\x=2\end{matrix}\right.\)

c) Ta có: \(2x^2-x-6=0\)

\(\Leftrightarrow2x^2-4x+3x-6=0\)

\(\Leftrightarrow2x\left(x-2\right)+3\left(x-2\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(2x+3\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-\dfrac{3}{2}\end{matrix}\right.\)

Câu 1: C

Câu 2: A

Câu 3: B

Câu 4:B

Câu 5: A

 Đặt \(x^2-2x=a\) thì \(x^2-2x-1=a-1\)

Ta có: \(\left(x^2-2x\right)\left(x^2-2x-1\right)-6\)

      \(=a\left(a-1\right)-6\)

      \(=a^2-a-6\)

      \(=a^2-3a+2a-6\)

      \(=a\left(a-3\right)+2\left(a-3\right)\)

      \(=\left(a+2\right)\left(a-3\right)\)

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

Cho mình hỏi: Bạn đã biết làm những bài bạn gửi chưa?

2 bài mình mới đăng là mh chỉ để lưu lại, lúc khác làm thôi, dù sao cx cảm ơn bạn 

dễ ẹc!!!!!!!!

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

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

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

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

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

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

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

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

     2x² + x - 6 

= 2x² + 4x - 3x - 6

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

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

dễ ẹc!!!!!!!!