SOLUTION: Why is {{{49y^2+16}}} prime, but {{{16y^2-49}}} isn't? Any tips on how I can tell if a polynomial is prime or not?

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Question 1031482: Why is 49y%5E2%2B16 prime, but 16y%5E2-49 isn't? Any tips on how I can tell if a polynomial is prime or not?
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
I assume by a prime polynomial you mean "factorable over the integers."

16y^2 - 49 is factorable since it is the difference of two squares, and can be written as (4y-7)(4y+7). But 49y^2 + 16 can't be factored over integers.

In general, determining whether a polynomial is factorable over integers is difficult, but sometimes you may be able to look for patterns, or find roots of the polynomial, etc.