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: 6

$(5x-2)(x-4)$

In accordance with the rules of factoring trinomials, we need to find two integers whose product is $40$ and whose sum is $-22$. A little searching determines that these numbers are $-2$ and $-20$. Therefore, we can express the middle term $-22x$ as $-2x-20x$ and proceed to factoring by grouping: $5x^{2}-22x+8$ =$5x^{2}-2x-20x+8$ =$x(5x-2)-4(5x-2)$ =$(5x-2)(x-4)$