Once again, we will do it the long way so you can see what is involved.

In this case, we need 2*n*^{2} so we start
with:

2*n*^{2} − 13*n* − 7 = (2*n* ... )(*n* ... )

Now we need 2 numbers that *multiply* to give −7 and the
sum of the **inner** and **outer products** must be −13.
**Don't forget the 2 in the first bracket**!

Possibility 1:−7 and 1

**Multiply** to give −7

2*n*^{2} − 13*n* − 7 = (2*n* − 7)(*n* + 1)

**Outer product plus inner product:**

(2*n*)(1) + (−7)(*n*) = 2*n* − 7*n* = −5*n*

This is not the correct answer.

Possibility 2:7 and −1

This would give us

Outer product plus inner product:

(2*n*)(−1) + (7)(*n*) = −2*n* + 7*n* = 5*n*

Possibility 3:−1 and 7

2*n*^{2} − 13*n* − 7 = (2*n* − 1)(*n* + 7)

Outer product plus inner product:

(2*n*)(7) + (−1)(*n*) = 14*n* − *n* = 13*n*

This is still not the correct answer.

Possibility 4:1 and −7

2*n*^{2} − 13*n* − 7 = (2*n* + 1)(*n* − 7)

Outer product plus inner product:

(2*n*)(−7) + (1)(*n*) = −14*n* + *n* = −13*n*

This is the required answer, finally.

So

2*n*^{2} − 13*n* − 7 = (2*n* + 1)(*n* − 7)

I repeat, it won't always involve several steps like this. The more you do them, the easier and quicker they become (like most new skills).