\(x^3-5x^2-9x+45=0\)
=>\(x^2\left(x-5\right)-9\left(x-5\right)=0\)
=>\(\left(x-5\right)\left(x^2-9\right)=0\)
=>\(\left(x-5\right)\left(x-3\right)\left(x+3\right)=0\)
=>\(\left[{}\begin{matrix}x-5=0\\x-3=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\\x=-3\end{matrix}\right.\)
`x^3 -5x^2 -9x+45=0`
`<=> (x^3 -5x^2 )-(9x-45)=0`
`<=> x^2 (x-5)- 9(x-5)=0`
`<=>(x-5)(x^2 -9)=0`
`<=>(x-5)(x-3)(x+3)=0`
\(\Leftrightarrow\left[{}\begin{matrix}x-5=0\\x-3=0\\x+3=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=5\\x=3\\x=-3\end{matrix}\right.\)
