Factorise:
`x ^(2) -11 x - 42`

Answer

To factorise the expression \( x^2 - 11x - 42 \), we can follow these steps:

### Step 1: Identify the coefficients
The given quadratic expression is \( x^2 - 11x - 42 \). Here, the coefficients are:
- Coefficient of \( x^2 \) (a) = 1
- Coefficient of \( x \) (b) = -11
- Constant term (c) = -42

### Step 2: Multiply \( a \) and \( c \)
We need to find two numbers that multiply to \( a \cdot c \) (which is \( 1 \cdot -42 = -42 \)) and add up to \( b \) (which is -11).

### Step 3: Find the two numbers
We are looking for two numbers that multiply to -42 and add to -11. The numbers that satisfy this condition are -14 and 3, since:
- \( -14 \times 3 = -42 \)
- \( -14 + 3 = -11 \)

### Step 4: Rewrite the middle term
Now, we can rewrite the expression \( x^2 - 11x - 42 \) using the two numbers we found:
\[ x^2 - 14x + 3x - 42 \]

### Step 5: Factor by grouping
Next, we will group the terms:
\[ (x^2 - 14x) + (3x - 42) \]
Now, we can factor out the common factors from each group:
\[ x(x - 14) + 3(x - 14) \]

### Step 6: Factor out the common binomial
Now, we can see that \( (x - 14) \) is a common factor:
\[ (x - 14)(x + 3) \]

### Final Answer
Thus, the factorised form of \( x^2 - 11x - 42 \) is:
\[ (x - 14)(x + 3) \]