Answer
prime
Work Step by Step
Rearranging the terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
2t^2-19-6t
\\\\=
2t^2-6t-19
.\end{array}
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
2t^2-6t-19
\end{array} has $ac=
2(-19)=-38
$ and $b=
-6
.$
There are no two numbers with a product of $c$ and a sum of $b.$ Hence, the expression is $\text{
prime
.}$