ANSWER
Prime
EXPLANATION
The given quadratic expression is
[tex] {2t}^{2} - 19 - 6t[/tex]
We rewrite in standard form to obtain
[tex]{2t}^{2} - 6t - 19[/tex]
Comparing to the standard quadratic function in t,
[tex]a {t}^{2} + bt + c[/tex]
We have
[tex]a = 2[/tex]
[tex]b = - 6[/tex]
[tex]c = - 19[/tex]
We find that the product
[tex]ac = 2 \times - 19 = - 38[/tex]
There are no two factors of -38 that sums up to -6.
This means that, the given polynomial does not have rational factors.
Therefore the polynomial is prime.
