# How do you factor 2x³+16x²+24x?

Nov 19, 2015

Separate out the common factor $2 x$, then find a pair of numbers whose sum is $8$ and whose product is $12$ to get:
$2 {x}^{3} + 16 {x}^{2} + 24 x = 2 x \left(x + 2\right) \left(x + 6\right)$
Notice that all of the terms are divisible by $2 x$, so separate that factor out first, Then notice that $2 + 6 = 8$ and $2 \times 6 = 12$, so:
$2 {x}^{3} + 16 {x}^{2} + 24 x = 2 x \left({x}^{2} + 8 x + 12\right) = 2 x \left(x + 2\right) \left(x + 6\right)$