The polynomial is
.
The general quadratic expression form is
.
In this trinomial
and
.
Find two numbers with a sum of
and a product of
.
Make a list of the factors of
and look for the of factors with the sum of
.

There are no factors with a product of
.
So, the quadratic expression can not be factored using integers.
\Therefore, the polynomial expression
is prime.
The polynomial expression
is prime.