trinomials that are prime over the set of rational numbers will NOT factor.
A Tinomial ax^2 + bx + c 'will factor' if (b^2-4ac)is a perfect square or zero.
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rational and prime numbers
No, it is not.
The set of rational numbers includes the set of natural numbers but they are not the same. All natural numbers are rational, not all rational numbers are natural.
The Real numbers
It is the rational numbers.