Question

Factor completely. If a polynomial is prime, state this.
2t^2-19-6t

Answer 1

Prime

Step-by-step explanation

The given quadratic expression is

`{2t}^(2) - 19 - 6t`

We rewrite in standard form to obtain

`{2t}^(2) - 6t - 19`

Comparing to the standard quadratic function in t,

`a {t}^(2) + bt + c`

We have

`a = 2`

`b = - 6`

`c = - 19`

We find that the product

`ac = 2 * - 19 = - 38`

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.