Question

Which of the following polynomials is prime over the set of rational numbers?

a.x^2-13x-36
b.x^2-5x-36
c.x^2+15x+36
d.x^2+20x+36

Answer 1

check to see for each of
\[b^2-4ac\] is a perfect square ( 0 counts as a perfect square)
if so, rational zeros.
if not, irrational zeros so prime over the rationals

Answer 2

for example in the first one
\[13^2-4\times 1\times (-36)=313\] which is not a perfect square.

Answer 3

where as in the second one
\[5^2+4\times 36=169\] which is a perfect square since it is the square of 13