Work:
To factor the trinomial 3a^(2)-8a-28, we can use the factoring method.
First, we need to find two numbers that multiply to give us -84 (the product of the coefficient of the squared term and the constant term) and add up to give us -8 (the coefficient of the linear term).
After some trial and error, we find that -14 and 6 satisfy these conditions.
Next, we can rewrite the trinomial as follows:
3a^(2)-14a+6a-28
Now, we can group the terms and factor by grouping:
(3a^(2)-14a)+(6a-28)
Taking out the greatest common factor from each group, we get:
a(3a-14)+2(3a-14)
Notice that we have a common binomial factor of (3a-14).
Factoring out this common factor, we get:
(3a-14)(a+2)
Therefore, the factored form of the trinomial 3a^(2)-8a-28 is (3a-14)(a+2).
We can conclude that the trinomial is not prime.