Factoring Trinomials of the type ax^2+bx+c

Question

2t²-19-6t

 

Factor completely

Answer 1

It's not factorable. It would be considered prime. There are two ways to check when you have a trinomial in the form of ax²+bx+c.

 

One way is to use a factoring method such as the AC-method, and you find it is impossible to find two factors of -38 that will add/subtract to get -6.

 

The second way uses B²-4AC. If you plug the numbers in and you get a zero or a positive square (i.e. 36 or 81), it is factorable. If not, it's prime.

 

Answer 2

For this, I would rewrite (ax² + bx + c)

 

2t² -6t -19

 

This is not factorable (unless there is typo).  So, that is the answer.