a, \(x^3-2x=0\Leftrightarrow x\left(x^2-2\right)=0\Leftrightarrow x=;x=\pm\sqrt{2}\)

b, \(x^2\left(x-3\right)+12-4x=0\Leftrightarrow x^2\left(x-3\right)-4\left(x-3\right)\)

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x-3\right)=0\Leftrightarrow x=\pm2;x=3\)

c, \(\left(x-2\right)^2=x^3-8=\left(x-2\right)\left(x^2+2x+4\right)\)

\(\Leftrightarrow\left(x-2\right)\left(x-2-x^2-2x-4\right)=0\Leftrightarrow\left(x-2\right)\left(-x^2-x-6\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(x^2+x+6>0\right)=0\Leftrightarrow x=2\)

d, \(x^2-5x+6=0\Leftrightarrow\left(x-2\right)\left(x-3\right)=0\Leftrightarrow x=2;x=3\)

e, \(x^3-4x^2+2x-1=0\Leftrightarrow x=3,5...\)

\(4ab-8a^2b=4ab\left(1-2a\right)\)

\(x^2-4+3xy-6y\)

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

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

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

\(x^2-8x+12\)

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

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

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

\(x^4+64\)

\(=x^4+16x^2+64-16x^{2^2}\)

\(=\left(x^2+8\right)^2-\left(4x\right)^2\)

\(=\left(x^2-4x+8\right)\left(x^2^2+4x+8\right)\)

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

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

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

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

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

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

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

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

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

\(x^5+x^4+1\)

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

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

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

ko vì tích của 3 số tự nhiên liên tiếp luôn là 1 số chẵn mà 3^50 là số lẻ nên mâu thuẫn.Do đó 3^50 ko là tích của 3 số tự nhiên liên tiếp

Trả lời:

1) sửa đề:  \(x^4+x^3-4x-4=x^3\left(x+1\right)-4\left(x+1\right)=\left(x+1\right)\left(x^3-4\right)\)

2) \(x^2-\left(a+b\right)x+ab=x^2-ax-bx+ab=\left(x^2-ax\right)-\left(bx-ab\right)\)

\(=x\left(x-a\right)-b\left(x-a\right)=\left(x-a\right)\left(a-b\right)\)

3)  \(5xy^3-2xyz-15y^2+6z=\left(5xy^3-15y^2\right)-\left(2xyz-6z\right)\)

\(=5y^2\left(xy-3\right)-2z\left(xy-3\right)=\left(xy-3\right)\left(5y^2-2z\right)\)

con lay bo ko tra loi thi thoi