Factor `n^(2)-5n-14`.

Answer

To factor the expression \( n^2 - 5n - 14 \), we will follow these steps:

### Step 1: Identify the coefficients
The expression is a quadratic trinomial of the form \( ax^2 + bx + c \), where:
- \( a = 1 \) (coefficient of \( n^2 \))
- \( b = -5 \) (coefficient of \( n \))
- \( c = -14 \) (constant term)

### Step 2: Find two numbers that multiply to \( ac \) and add to \( b \)
We need to find two numbers that multiply to \( ac = 1 \times (-14) = -14 \) and add to \( b = -5 \).

The two numbers that satisfy these conditions are \( -7 \) and \( 2 \):
- \( -7 \times 2 = -14 \)
- \( -7 + 2 = -5 \)

### Step 3: Rewrite the middle term using the two numbers
We can rewrite the expression \( n^2 - 5n - 14 \) as:
\[ n^2 - 7n + 2n - 14 \]

### Step 4: Factor by grouping
Now we will group the terms:
\[ (n^2 - 7n) + (2n - 14) \]

Next, we factor out the common factors from each group:
- From \( n^2 - 7n \), we can factor out \( n \):
\[ n(n - 7) \]
- From \( 2n - 14 \), we can factor out \( 2 \):
\[ 2(n - 7) \]

Now we can combine these factored terms:
\[ n(n - 7) + 2(n - 7) = (n - 7)(n + 2) \]

### Step 5: Write the final factored form
Thus, the expression \( n^2 - 5n - 14 \) can be factored as:
\[ (n - 7)(n + 2) \]

### Final Answer
The factored form of \( n^2 - 5n - 14 \) is:
\[ (n - 7)(n + 2) \]

---