5. \(3x^2-5x-8=0\Leftrightarrow3x^2+3x-8x-8=0\)
\(\Leftrightarrow3x\left(x+1\right)-8\left(x+1\right)=0\Leftrightarrow\left(x+1\right)\left(3x-8\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x+1=0\\3x-8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=\dfrac{8}{3}\end{matrix}\right.\)
6. \(x^2-x-12=0\Leftrightarrow x^2-4x+3x-12=0\)
\(\Leftrightarrow x\left(x-4\right)+3\left(x-4\right)=0\Leftrightarrow\left(x-4\right)\left(x+3\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=-3\end{matrix}\right.\)
8. \(x^2-x-\left(3x-3\right)=0\Leftrightarrow x\left(x-1\right)-3\left(x-1\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-3\right)=0\Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=3\end{matrix}\right.\)
9. \(x^2-16x=0\Leftrightarrow x\left(x-16\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=16\end{matrix}\right.\)
10. \(x^2-25x=0\Leftrightarrow x\left(x-25\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x=25\end{matrix}\right.\)
7. \(x^3-2x^2-x+2=0\Leftrightarrow x^2\left(x-2\right)-\left(x-2\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x^2-1\right)=0\Leftrightarrow\left(x-2\right)\left(x+1\right)\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+1=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-1\\x=1\end{matrix}\right.\)
