Q. 254 - Intermediate Algebra

Question

In the following exercises, factor completely. 

$12ab-6a+10b-5$

Step-by-Step Solution

Answer

The required factors are $(6a+5)(2b-1)$

Step 1. Given Information

The given expression is $12ab-6a+10b-5$

Step 2. Calculation

We will find the factors by grouping the terms with common factors and then factor out the common factors from each group.

$$\begin{gathered} 12ab-6a+10b-5=(12ab-6a)+(10b-5) \\ =6a(2b-1)+5(2b-1) \\ =(6a+5)(2b-1) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} (6a+5)(2b-1)=6a(2b-1)+5(2b-1) \\ =(12ab-6a)+(10b-5) \\ =12ab-6a+10b-5 \end{gathered}$$