Answer
$(x+3)(x+4)(x-4)$
Work Step by Step
Using factoring by grouping, the factored form of the given expression, $
x^3+3x^2-16x-48
,$
\begin{array}{l}
(x^3+3x^2)-(16x+48)
\\\\=
x^2(x+3)-16(x+3)
\\\\=
(x+3)(x^2-16)
.\end{array}
Using $a^2-b^2=(a+b)(a-b)$ or the factoring of the difference of $2$ squares, then the factored form of the expression, $
(x+3)(x^2-16)
$, is
\begin{array}{l}
(x+3)(x+4)(x-4)
.\end{array}