Question

giúp mk nha khẩn cấp

Answer 1

5) \(x^6-7x^3-8=x^3\left(x^3-8\right)+x^3-8=\left(x^3+1\right)\left(x^3-8\right)\)

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

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

Đặt t = \(x^2-x\)  ; ta có : \(t^2+t-6=t\left(t+3\right)-2\left(t+3\right)=\left(t-2\right)\left(t+3\right)\)

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

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

7) \(x^2\left(x^2-7\right)^2-36=\left[x\left(x^2-7\right)-6\right]\left[x\left(x^2-7\right)+6\right]\)

\(=\left[x^3-7x-6\right]\left[x^3-7x+6\right]\) 

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

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

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

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

Answer 2

8) \(49x^2-\left(3x+2\right)^2=\left(7x-3x-2\right)\left(7x+3x+2\right)\)

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

9) \(x^4-10x^2+9=x^2\left(x^2-9\right)-\left(x^2-9\right)\)

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