## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

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 $\text{ prime .}$