How do you factor 5x^2(x - 10) + (x - 10)?

$\left(x - 10\right) \left(5 {x}^{2} + 1\right)$
$\text{take out the "color(blue)"common factor"" of } \left(x - 10\right)$
$\Rightarrow \textcolor{red}{5 {x}^{2}} \left(x - 10\right) \textcolor{red}{+ 1} \left(x - 10\right)$
$= \left(x - 10\right) \left(\textcolor{red}{5 {x}^{2} + 1}\right)$