Answer
$$-(x^2+1)(3x-1)(3x+1).$$
Work Step by Step
First, for the polynomial $1 - 8x^2 - 9x^4$, we write
$$
1 - 8x^2 - 9x^4=-(9x^4+8x^2-1)=-(9x^4+9x^2-x^2-1)
.$$
By grouping the first two terms and the second two terms and then taking common factors, we have
$$-(9x^4+9x^2-x^2-1) =-(9x^2(x^2+1)-(x^2+1))\\
=-(x^2+1)(9x^2-1) .$$
The polynomial $x^2+1$ can not be factored because it is prime. The remaining terms can be factored as follows:
$$9x^2-1=(3x-1)(3x+1)$$
where we recognized the difference of two squares $(a-b)(a+b)=a^2-b^2$.
