Answer
$-2(2x+1)(2x-1)(x^2+2)$
Work Step by Step
Let $x^2=a$.
$4-14x^2-8x^4=4-14a-8a^2$
Factor out $2$.
$=2(2-7a-4a^2)$
Rewrite $-7a$ as $-8a+1a$
$=2(2-8a+1a-4a^2)$
Group the first two terms together and group the last two terms together.
$=2[(2-8a)+(1a-4a^2)]$
Factor out the GCF in each group.
$=2[2(1-4a)+a(1-4a)]$
Factor out $(1-4a)$.
$=2(1-4a)(2+a)$
Back substitute $a=x^2$.
$=2(1-4x^2)(2+x^2)$
$=2[1^2-(2x)^2](2+x^2)$
Use special formula $a^2-b^2=(a+b)(a-b)$ wehere $a=1$ and $b=2x$.
$=2(1+2x)(1-2x)(2+x^2)$
$=2(2x+1)[-(-1+2x)](x^2+2)$
$=-2(2x+1)(2x-1)(x^2+2)$
Hence, the completely factored form of the given expression is $-2(2x+1)(2x-1)(x^2+2)$.
