Answer
$5r(2r+1)(r+3)$
Work Step by Step
$10r^{4}+30r^{3}+5r^{2}+15r=$
...factor out the GCF:
$10r^{4}=2\cdot(5)\cdot(r)\cdot r\cdot r\cdot r$
$30r^{3}=2\cdot 3\cdot(5)\cdot(r)\cdot r\cdot r$
$5r^{2}=(5)\cdot(r)\cdot r$
$15r=3\cdot(5)\cdot(r)$
GCF: $5r$
$=5r(2r^{2}+6r+r+3)$
...factor by grouping.
$=5r[2r(r+3)+1(r+3)]$
...factor again.
$=5r(2r+1)(r+3)$
