Factorise :
`x^(2) - 5x -6`

Answer

To factorise the expression \( x^2 - 5x - 6 \), we will use the splitting the middle term method. Here are the steps:

### Step 1: Identify the coefficients
The expression is \( x^2 - 5x - 6 \). Here, the coefficients are:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = -5 \) (coefficient of \( x \))
- \( c = -6 \) (constant term)

### Step 2: Find two numbers that multiply to \( a \cdot c \) and add to \( b \)
We need to find two numbers that multiply to \( a \cdot c = 1 \cdot (-6) = -6 \) and add to \( b = -5 \).

The two numbers that satisfy these conditions are:
- \( -6 \) and \( 1 \) (since \( -6 + 1 = -5 \) and \( -6 \cdot 1 = -6 \))

### Step 3: Rewrite the middle term using the two numbers
We can now rewrite the expression \( -5x \) as \( -6x + 1x \):
\[ x^2 - 6x + 1x - 6 \]

### Step 4: Group the terms
Next, we group the terms:
\[ (x^2 - 6x) + (1x - 6) \]

### Step 5: Factor out the common factors from each group
Now we factor out the common factors from each group:
\[ x(x - 6) + 1(x - 6) \]

### Step 6: Factor out the common binomial factor
Now, we can factor out the common binomial factor \( (x - 6) \):
\[ (x - 6)(x + 1) \]

### Final Result
Thus, the factorised form of \( x^2 - 5x - 6 \) is:
\[ (x - 6)(x + 1) \]

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