1) x³ + 2x² + 2x + 4 = 0

x² ( x + 2 ) + 2 ( x + 2 ) = 0

( x² + 2 ) ( x + 2 ) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x^2+2=0\\x+2=0\end{matrix}\right.\)

\(\Leftrightarrow x=-2\)

2) x³ + 4x² - 2x - 8 = 0

x² ( x + 4 ) - 2 ( x + 4 ) = 0

( x² - 2 ) ( x + 4 ) = 0

\(\Leftrightarrow\left[{}\begin{matrix}x^2-2=0\\x+4=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\pm\sqrt{2}\\x=-4\end{matrix}\right.\)