Is x squared plus 12x plus 28 prime?

Answer 1

Looking at the function:

x2 + 12x + 28

We know that in order to factor it, we would need two numbers whose product is equal to 28 and whose sum is equal to twelve. We know they must both be positive, as both their sum and their product are positive. That means our possible numbers to combine are all the positive factors of 28:

1, 2, 4, 7, 14, 28

As it happens, no two of these will add up to 12, which tells us that yes, the original polynomial is prime.