Answer
$-(4x+1)(4x-5)$
Work Step by Step
Write the given expression in standard form to obtain:
$5+16x-16x^2=-16x^2+16x+5$
Factor out $-1$ to obtain:
$=-1(16x^2-16x-5)\\
=-(16x^2-16x-5)$
Rewrite $16x$ as $4x-20x$.
$=-(16x^2-4x-20x-5)$
Group the first two terms together and group the last two terms together to obtain:
$=-[(16x^2+4x)+(-20x-5)]$
Factor out the GCF in each group.
$=-[4x(4x+1)+(-5)(4x+1)$
$=-[4x(4x+1)-5(4x+1)$
Factor out $(4x+1)$.
$=-[(4x+1)(4x-5)]$
$=-(4x+1)(4x-5)$
Hence, the completely factored form of the given expression is $-(4x+1)(4x-5)$.
