Chapter 6 - Factoring, Solving Equations, and Problem Solving - 6.4 - Factoring Trinomials of the Form ax^2+bx+c - Problem Set 6.4 - Page 261: 5

$(4x-1)(x-6)$

In accordance with the rules of factoring trinomials, we need to find two integers whose product is $24$ and whose sum is $-25$. A little searching determines that these numbers are $-1$ and $-24$. Therefore, we can express the middle term $-25x$ as $-1x-24x$ and proceed to factoring by grouping: $4x^{2}-25x+6$ =$4x^{2}-1x-24x+6$ =$x(4x-1)-6(4x-1)$ =$(4x-1)(x-6)$