$\displaystyle x^5+x^3+x$
Answer: $\displaystyle x(1-x+x^2)(1+x+x^2)$
$\displaystyle \begin{aligned}
x^5+x^3+x &= x(x^4 + {\color{blue}x^2} + 1) \\
&= x(x^4\;{\color{red}+\;2x^2} + 1\;{\color{red}-\;x^2}) \\
\end{aligned}$
...
Do you see the x-squared term in the previous step that I colored in blue? I replaced that with $\displaystyle 2x^2 - x^2$, which is in red and separated. After all, $\displaystyle x^2 = 2x^2 - x^2$.
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