Answer
$(x+3)(x+1)(x-1)(x^2-3x+9)$.
Work Step by Step
The given expression is
$=x^5-x^3+27x^2-27$
Group terms.
$=(x^5-x^3)+(27x^2-27)$
Factor from each group.
$=x^3(x^2-1)+27(x^2-1)$
Factor out $(x^2-1)$.
$=(x^2-1)(x^3+27)$
$=(x^2-1^2)(x^3+3^3)$
Use algebraic identity.
$(a^2-b^2)=(a-b)(a+b)$
The second term will be
$(x^2-1^2)=(x-1)(x+1)$
and $(a^3+b^3)=(a+b)(a^2-ab+b^2)$
The first term will be
$(x^3+3^3)=(x+3)(x^2-3x+9)$
Plug all values.
$=(x-1)(x+1)(x+3)(x^2-3x+9)$
Rearrange.
$=(x+3)(x+1)(x-1)(x^2-3x+9)$.
