Chapter 6 - Section 6.1 - The Greatest Common Factor and Factoring by Grouping - Exercise Set - Page 427: 37

$50y^2(2y^3-y+2)$

Factoring the $GCF= 50y^2 ,$ the given expression, $ 100y^5-50y^3+100y^2 ,$ is equivalent to \begin{array}{l}\require{cancel} 50y^2 \left( \dfrac{100y^5}{50y^2}-\dfrac{50y^3}{50y^2}+\dfrac{100y^2}{50y^2} \right) \\\\= 50y^2(2y^3-y+2) .\end{array}