Answer
$-3x(2x+1)(4x+7)$
Work Step by Step
For the polynomial
$$
-24x^3 -54x^2 -21x=-3x(8x^2+18x+7)
$$
we check the factors of $ac=8(7)=56$. The only factors that can give the right middle term are $14$ and $4$, as follows
$$
-3x(8x^2+18x+7)=-3x(2x+1)(4x+7)
.$$
