Answer
$(x+1)(x-1)(x-2)(x^2+2x+4)$.
Work Step by Step
The given expression is
$=x^5-x^3-8x^2+8$
Rearrange.
$=x^5-8x^2-x^3+8$
Group terms.
$=(x^5-8x^2)+(-x^3+8)$
Factor from each group.
$=x^2(x^3-8)-1(x^3-8)$
Factor out $(x^3-8)$.
$=(x^3-8)(x^2-1)$
$=(x^3-2^3)(x^2-1^2)$
Use algebraic identity.
$(a^3-b^3)=(a-b)(a^2+ab+b^2)$
The first term will be
$(x^3-2^3)=(x-2)(x^2+2x+4)$
and $(a^2-b^2)=(a-b)(a+b)$
The second term will be
$(x^2-1^2)=(x-1)(x+1)$
Plug all values.
$=(x-2)(x^2+2x+4)(x-1)(x+1)$
Rearrange.
$=(x+1)(x-1)(x-2)(x^2+2x+4)$.
