Answer
The polynomial is prime.
Work Step by Step
Factor out $-1$ to obtain:
$14+6x-x^2
\\=-1(-14-6x+x^2)
\\=-1(x^2-6x-14)$
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 $b=-6$ and $c=-14$.
Note that $-14$ has no factors whose sum is $-6$.
Thus, the given expression is prime.
