Answer
$x^3-4x^2-21x=x(x-7)(x+3)$
Work Step by Step
Factor out the GCF $x$ to get
$\\=x(x^2-4x-21)$.
Factor the trinomial to get
$\\=x(x-7)(x+3)$.
Check by multiplying the factors:
$=x(x^2+3x-7x-21)
\\=x(x^2-4x-21)
\\=x^3-4x^2-21x$.