Answer
$x(x+3)(x^{2}-3x+9)$
Work Step by Step
$ x^{4}+27x\qquad$...factor out the common term, $x$
$=x(x^{3}+27)\qquad$...use the sum of two cubes: $\mathrm{A}^{3}+\mathrm{B}^{3} = (\mathrm{A}+\mathrm{B})(\mathrm{A}^{2} - \mathrm{A}\mathrm{B} + B^{2})$
$=x(x^{3}+3^{3})$
$=x(x+3)(x^{2}-3x+9)$
