Answer
$-(x+3)(x-5)$
Work Step by Step
Write the given expression in standard form to obtain:
$15+2x-x^2=-x^2+2x+15$
Factor out $-1$:
$=-1(x^2-2x-15)$
$=-(x^2-2x-15)$
Look for factors of $-15$ whose sum is equal t the middle term's coefficient ($-2$). The factors are $-5$ and $2$.
Rewrite $-2x$ as $3x-5x$.
$=-(x^2+3x-5x-15)$
Group the first two terms together and group the last two terms together to obtain:
$=-[(x^2+3x)+(5x-15)]$
Factor out the GCF in each group.
$=-[x(x+3)+(-5)(x+3)]$
$=-[x(x+3)-5(x+3)]$
Factor out $(x+3)$.
$=-(x+3)(x-5)$
Hence, the completely factored form of the given expression is $-(x+3)(x-5)$.
