Answer
This polynomial is prime.
Work Step by Step
$x^2+9xy+16y^2$
This polynomial is prime because the perfect square trinomial formula says that
$(A±B)^2=A^2±2AB+B^2$
In the given example, $2AB=9xy≠2×x×4y$.
If it were a perfect square trinomial, the middle term would be $8xy$.
