\(a,2x\left(x^3-3\right)-2x^4=18\\ 2x^4-6x-2x^4=18\\ -6x=18\\ x=-3\)

\(b,9x\left(4-x\right)+\left(3x+1\right)^2=2\\ 36x-9x^2+9x^2+6x+1=2\\ 42x=2-1\\ 42x=1\\ x=\dfrac{1}{42}\)

\(a,3x^2-12xy=3x\left(x-4y\right)\)

\(b,x^2+7x-2\left(x+7\right)=x\left(x+7\right)-2\left(x+7\right)=\left(x+7\right)\left(x-2\right)\)

\(c,8x^3-8x^2+2x\\ =2x\left(4x^2-4x+1\right)\\ =2x\left(2x-1\right)^2\)

\(d,x^2-y^2+12y-36\\ =x^2-\left(y^2-12y+36\right)\\ =x^2-\left(y-6\right)^2=\left(x+y-6\right)\left(x-y+6\right)\)

\(a,\left(2x-3\right)^2-4x\left(x-3\right)\\ =4x^2-12x+9-4x^2+12x\\ =\left(4x^2-4x^2\right)+\left(-12x+12x\right)+9\\ =9\)

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

\(a,\left(x-y-z\right)^5:\left(x-y-z\right)^3=\left(x-y-z\right)^2\)

\(b,\left(x^2+2x+x^2-4\right):\left(x+2\right)\\ =\left[x\left(x+2\right)+\left(x-2\right)\left(x+2\right)\right]:\left(x+2\right)\\ =\left[\left(x+2\right)\left(x+x-2\right)\right]:\left(x+2\right)\\ =2x-2\)

\(A=\dfrac{x^2+2x-3}{x+3}=\dfrac{x^2-x+3x-3}{x+3}=\dfrac{x\left(x-1\right)+3\left(x-1\right)}{x+3}=\dfrac{\left(x-1\right)\left(x+3\right)}{x+3}=x-1\)

Xét ΔABC có: D, E lần lượt là trung điểm của AB,BC

=> DE là đường trung bình của ΔABC 

=> DE  \(=\dfrac{1}{2}\)AC => DE  \(=\dfrac{1}{2}.8=4\) cm

Chọn đáp án D. 4 cm