Question

Create your own prime trinomial in the form ax2 + bx + c. Using complete sentences, explain how you know it is prime

Answer 1

Since the factors of 3b^2 are 3b and b, you could set up an expression like this:
(3b+x)(b+y) 3y and x will add to 8, and x(y) will multiply to 4
(3b+2)(b+2) simplify this
(3b^2+6b+2b+4 simplify further
3b^2+8b+4 and there is your starting answer. therefore the factors are (3b+2)(b+2)

to create a prime trinomial set a as 1 and then find a b and c that don't factor like b=5, c=2

Answer 2

Just as a note: We know a prime polynomial is prime if the only factors if the polynomial are 1 and itself.