Q. 245 - Intermediate Algebra

Question

In the following exercises, factor completely. 

$7b^2+7b-42$

Step-by-Step Solution

Answer

The required factors are $7(b+3)(b-2)$

Step 1. Given Information

The given expression is $7b^2+7b-42$

Step 2. Calculation

We will find the factors by first factor out the common term and then use the middle term splitting method.

$$\begin{gathered} 7b^2+7b-42=7(b^2+b-6) \\ =7(b^2+3b-2b-6) \\ =7\left(b\right(b+3)-2(b+3\left)\right) \\ =7(b+3)(b-2) \end{gathered}$$

Step 3. Check

We will verify the factors by multiplying the factors.

$$\begin{gathered} 7(b+3)(b-2)=7\left(b\right(b+3)-2(b+3\left)\right) \\ =7(b^2+3b-2b-6) \\ =7(b^2+b-6) \\ =7b^2+7b-42 \end{gathered}$$