Answer
$$-2(2x-1)(2x+1)(x^2+2) .$$
Work Step by Step
First, for the polynomial $4 - 14x^2 - 8x^4$, we write
$$
4 - 14x^2 - 8x^4=-2(4x^4+7x^2-2)=-2(4x^4-x^2+8x^2-2)
.$$
By grouping the first two terms and the second two terms and then taking common factors, we have
$$-2(4x^4-x^2+8x^2-2) =-2(x^2(4x^2-1)+2(4x^2-1))\\
=-2(4x^2-1)(x^2+2) .$$
The polynomial $x^2+2$ can not be factored because it is prime.
The remaining terms can be factored as follows:
$$4x^2-1=(2x-1)(2x+1)$$
where we recognized the difference of two squares $(a-b)(a+b)=a^2-b^2$.
Thus we have:
$$-2(2x-1)(2x+1)(x^2+2) .$$
