Question

In the following exercises, factor completely.$2n^2+13n-7$

Short answer

The required factors are$(2n-1)(n+7)$

Step-by-step solution

Step 1. Given Information

The given expression is$2n^2+13n-7$

Step 2. Calculation

We will use the middle term splitting method to find the factors.

$$\begin{gathered} 2n^2+13n-7=2n^2+14n-n-7 \\ =2n(n+7)-1(n+7) \\ =(2n-1)(n+7) \end{gathered}$$

Step 3. Check

We will verify the result by multiplying the factors.

$$\begin{gathered} (2n-1)(n+7)=2n(n+7)-1(n+7) \\ =2n^2+14n-n-7 \\ =2n^2+13n-7 \end{gathered}$$