Factorise:
`x^(2) + x-56`

Answer

To factorise the expression \( x^2 + x - 56 \), we will follow these steps:

### Step 1: Identify the coefficients
The expression is in the form \( ax^2 + bx + c \), where:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = 1 \) (coefficient of \( x \))
- \( c = -56 \) (constant term)

### Step 2: Find two numbers that multiply to \( ac \) and add to \( b \)
We need to find two numbers that multiply to \( a \cdot c = 1 \cdot (-56) = -56 \) and add to \( b = 1 \).

### Step 3: List factor pairs of \(-56\)
The factor pairs of \(-56\) that we can consider are:
- \( (1, -56) \)
- \( (-1, 56) \)
- \( (2, -28) \)
- \( (-2, 28) \)
- \( (4, -14) \)
- \( (-4, 14) \)
- \( (7, -8) \)
- \( (-7, 8) \)

### Step 4: Identify the correct pair
We need a pair that adds up to \( 1 \). The pair \( (8, -7) \) works because:
- \( 8 + (-7) = 1 \)
- \( 8 \times (-7) = -56 \)

### Step 5: Rewrite the middle term
We can rewrite the expression \( x^2 + x - 56 \) using the numbers we found:
\[ x^2 + 8x - 7x - 56 \]

### Step 6: Group the terms
Now, we group the terms:
\[ (x^2 + 8x) + (-7x - 56) \]

### Step 7: Factor by grouping
Factor out the common terms in each group:
\[ x(x + 8) - 7(x + 8) \]

### Step 8: Factor out the common binomial
Now, we can factor out the common binomial \( (x + 8) \):
\[ (x + 8)(x - 7) \]

### Final Result
Thus, the factorised form of the expression \( x^2 + x - 56 \) is:
\[ (x + 8)(x - 7) \]