Let be a prime. How do we show that the number of reducible polynomials over of the form is ?
I just know that is a field, and a polynomial of the form is of degree 2, so there is a theorem which says a polynomial of degree 2 or 3 is reducible over a field if and only if it has a root in that field.
So how can I show the total number of polynomials which have a zero in is ? Any help would be appreciated.