Question 1208160
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It is obvious that this is a middle school student, Ikleyn, not a junior in 
college. No junior in college is going to post a simple quadratic like
x^2 + 5x + 7.

I googled "proving that a polynomial is prime", and that told me that this is
an introductory middle school student in beginning factoring. Link to this video
will reveal what they're doing these days in middle school.

https://www.nagwa.com/en/videos/608139257981/#:~:text=In%20order%20to%20determine%20whether,%F0%9D%91%A5%20squared%20equal%20to%20one.

Go there are watch the video for kids in middle school.  It is verbatim with
what I posted above only with a different simple quadratic.

Ikleyn over-judged the maturity of this student.  If the student were an
advanced student, the question would be concerning prime and factorizable
general polynomials over rings, not a simple monic quadratic.  

Edwin</pre>