Answer
$$x(x^2 + 4)(x + 2)(x - 2)$$
Work Step by Step
For this expression, we can see that we can factor an $x$ from the expression to get:
$$x(x^4 - 16)$$
Looking at the polynomial, we can see that it is a difference of two squares. The difference of two squares can be factored as follows:
$$A^2 - B^2 = (A - B)(A + B)$$
where $A$ is the square root of the leading term and $B$ is the square root of the second term.
In this case, we see that $A$ is $\sqrt x^4$ or $x^2$ and $B$ is $\sqrt 16$ or $4$. We plug these values into the formula:
$$x(x^2 + 4)(x^2 - 4)$$
We see that the $x^2 - 4$ can be factored even further because it also is a difference of squares. We use the same formula $(A + B)(A - B)$. In this case, $A$ is $\sqrt x^2$ or $x$ and $B$ is $\sqrt 4$ or $2$:
$$x(x^2 + 4)(x + 2)(x - 2)$$
