Factorise:
`28-31 x - 5x ^(2)`

Answer

To factorise the expression \( 28 - 31x - 5x^2 \), we will follow these steps:

### Step 1: Rearranging the Expression
First, we rearrange the expression in standard form:
\[ -5x^2 - 31x + 28 \]

### Step 2: Factor out the Negative Sign
Next, we can factor out a negative sign from the entire expression:
\[ -(5x^2 + 31x - 28) \]

### Step 3: Multiply the Coefficient of \(x^2\) and the Constant Term
Now, we need to multiply the coefficient of \(x^2\) (which is 5) by the constant term (which is 28):
\[ 5 \times 28 = 140 \]

### Step 4: Finding Two Numbers
We need to find two numbers that multiply to 140 and add up to -31 (the coefficient of \(x\)). The numbers we are looking for are -35 and +4 because:
\[ -35 \times 4 = -140 \quad \text{and} \quad -35 + 4 = -31 \]

### Step 5: Rewrite the Middle Term
Now, we can rewrite the expression by replacing -31x with -35x + 4x:
\[ -(5x^2 - 35x + 4x - 28) \]

### Step 6: Grouping Terms
Next, we group the terms:
\[ -[(5x^2 - 35x) + (4x - 28)] \]

### Step 7: Factor out Common Terms
Now we factor out the common terms from each group:
\[ -[(5x(x - 7) + 4(x - 7))] \]

### Step 8: Factor by Grouping
Now we can factor out the common binomial factor \((x - 7)\):
\[ -(x - 7)(5x + 4) \]

### Final Result
Thus, the factorised form of the expression \( 28 - 31x - 5x^2 \) is:
\[ -(x - 7)(5x + 4) \]