College Algebra, Chapter 1, 1.5, Section 1.5, Problem 8

Find all real solutions of the equation $x^5 - 16x = 0$


$
\begin{equation}
\begin{aligned}

x^5 - 16x =& 0
&& \text{Given}
\\
\\
x(x^4 - 16) =& 0
&& \text{Factor out } x
\\
\\
x(x^2 - 4)(x^2 + 4) =& 0
&& \text{Difference of squares}
\\
\\
x =& 0, x^2 - 4 = 0 \text{ and } x^2 + 4 = 0
&& \text{Zero Product Property}
\\
\\
x =& 0, x = \pm 2 \text{ and } x = \pm \sqrt{-4}
&& \text{Solve for } x
\\
\\
x =& 0, x = 2 \text{ and } x = -2
&& \text{All real solutions}


\end{aligned}
\end{equation}
$