Answer
$(x-3)^{2}(x+3)$
Work Step by Step
$ x^{3}-3x^{2}-9x+27\qquad$...factor in pairs.
$=(x^{3}-3x^{2})+(-9x+27)$
$=x^{2}(x-3)-9(x-3)$
$=(x-3)(x^{2}-9)\qquad$...recognize the difference of two squares: $a^{2}-b^{2}=(a-b)(a+b)$
$=(x-3)(x-3)(x+3)$
$=(x-3)^{2}(x+3)$
