algebra help?

Question

Is the trinomial b^2 + 3b + 29 a prime or not?

Answer 1

No sometimes it is prime but some times it is not why?

if b%3 =0 => (b+3)%3=0 => (b^2 + 3b)%3=0 => it is prime when b%3=0 coz 29 is prime

If b%3=1 or 2 => (b+3)%2= 1 or 2 => (b^2+3b)%3=1 => it is not prime cox 29+1=30 (30%3=0)

Hence, if b%3=0: it is prime
if b%3=1,2: it is not prime
Prove by urself by apply: b=1,2,3,4,5,6

Answer 2

Yes, it is prime (over the integers). There are no factors of 29 that add to 3.

Answer 3

It can be factored only over the complex numbers