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

Answer

To factorise the expression \( x^2 + 5x - 6 \), we will use the method of splitting the middle term. Here’s a step-by-step solution:

### Step 1: Identify the coefficients
The given quadratic expression is \( x^2 + 5x - 6 \). We identify:
- The coefficient of \( x^2 \) (which is 1),
- The coefficient of \( x \) (which is 5),
- The constant term (which is -6).

### Step 2: Calculate the product of the coefficient of \( x^2 \) and the constant term
We need to find two numbers that multiply to give the product of the coefficient of \( x^2 \) (which is 1) and the constant term (which is -6). Thus, we calculate:
\[ 1 \times (-6) = -6 \]

### Step 3: Find two numbers that multiply to -6 and add up to 5
We need to find two numbers that multiply to -6 and add up to 5. The numbers that satisfy this condition are 6 and -1, since:
\[ 6 \times (-1) = -6 \quad \text{and} \quad 6 + (-1) = 5 \]

### Step 4: Rewrite the middle term using these numbers
Now, we can rewrite the expression by splitting the middle term \( 5x \) into \( 6x - 1x \):
\[ x^2 + 6x - 1x - 6 \]

### Step 5: Group the terms
Next, we group the terms:
\[ (x^2 + 6x) + (-1x - 6) \]

### Step 6: 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 7: Factor by grouping
Now, we can factor out the common binomial factor \( (x + 6) \):
\[ (x - 1)(x + 6) \]

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

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