Answer
$(x-3)(x+3)(x^2+9)$
Work Step by Step
We have $ x^4-81=x^4-3^4$. The polynomial $x^4-3^4$ is a difference of two squares. That is, by using the fact that $a^2-b^2=(a-b)(a+b)$, we have
$$
x^4-3^4=(x^2-3^2)(x^2+3^2)=(x-3)(x+3)(x^2+9)
.$$
Moreover, the polynomial $x^2+9$ is a prime polynomial and can not be factored further.
