#### Answer

prime

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To factor the given expression, $
4t^2-3t+15
,$ find two numbers whose product is $ac$ and whose sum is $b$ in the quadratic expression $ax^2+bx+c.$ Use these $2$ numbers to decompose the middle term of the given quadratic expression and then use factoring by grouping.
$\bf{\text{Solution Details:}}$
Using factoring of trinomials, the value of $ac$ in the trinomial expression above is $
4(15)=60
$ and the value of $b$ is $
-3
.$ There are no $2$ numbers that have a product of $ac$ and a sum of $b.$ Hence the given trinomial is not factorable or it is $\text{
prime
.}$