Question

In the following exercises, factors completely:

$8m^2+22m+5$.

Short answer

The factors for the expression is,$(4m+1)(2m+5)$.

Step-by-step solution

Step 1. Given Information.

The expression is,

$8m^2+22m+5$.

Step 2. Factor completely.

Splitting the middle term such that the sum of the terms is $22$and the product of the terms is $40$,

$8m^2+22m+5=8m^2+2m+20m+5$

$$\begin{gathered} =(8m^2+2m)+(20m+5) \\ =2m(4m+1)+5(4m+1) \\ =(4m+1)(2m+5) \end{gathered}$$