## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$(x-3)(x+3)(x^2+9)$
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.