why is X squared + 9 prime?

Question

why is it prime?

Answer 1

It is not necessarily prime.  Here is a counter-example:

 

x = 3

 

x² + 9 = 3² + 9 = 18 = 2 · 3²

 

Note that

 

2 · 3² is not prime.

 

However, if x = 2, then

 

x² + 9 = 2² + 9 = 13,

 

which is prime.  The statement "x² + 9 is prime" is true for some values of x, but not for all values of x.