Answer
$-1(x-5)(x+3)$
Work Step by Step
Factor out $-1$ to obtain:
$15+2x-x^2
\\=-1(-15-2x+x^2)
\\=-1(x^2-2x-15)$
RECALL:
A trinomial of the form $x^2+bx+c$ can be factored if there are integers $d$ and $e$ such that $c=de$ and $b=d+e$.
The trinomial's factored form will be:
$x^2+bx+c=(x+d)(x+e)$
The trinomial above has $b=-2$ and $c=-15$.
Note that $-15=-5(3)$ and $-2= (-5)+3$.
This means that $d=-5$ and $e=3$
Thus, the factored form of the trinomial is:
$(x-5)(x+3)$
Therefore, the completely factored form of the given expression is:
$-1(x-5)(x+3)$
