# How do you factor  3x^3+21x^2+30x?

$3 {x}^{3} + 21 {x}^{2} + 30 x = 3 x \left(x + 2\right) \left(x + 5\right)$
First notice that all of the terms are divisible by $3 x$, so separate that out as a factor. Then note that $7 = 2 + 5$ and $10 = 2 \times 5$, so use that to factor the remaining quadratic:
$3 {x}^{3} + 21 {x}^{2} + 30 x = 3 x \left({x}^{2} + 7 x + 10\right) = 3 x \left(x + 2\right) \left(x + 5\right)$