#### Answer

prime

#### Work Step by Step

To factor when the coefficient of the first term is greater than $1$, first check if you can pull the greatest common factor from the terms. Then determine the two numbers that, when multiplied, equal the coefficient of the first term times the third term, and, when added, equal the coefficient of the middle term. Here, this polynomial meets none of the requirements, so it is prime.
$6x^2+2x+5$
is prime.