## Intermediate Algebra: Connecting Concepts through Application

$\bf{\text{Solution Outline:}}$ 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 $\text{ prime .}$