MHB Is a^2 - 6a + 12 Irreducible Over the Integers?

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In the textbook, the author showed that 8 + (a - 2)^3 factors out to be a(a^2 - 6a + 12).

The author goes on to say "...the expression a^2 - 6a + 12 is irreducible over the integers."

What does the author means by the statement?
 
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It simply means that the polynomial $a^2-6a+12$ cannot be factored into the product of two polynomials with coefficients that are integers. :D
 
Can you provide me with a few more irreducible examples?
 

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