Factorise :
`2x^(2) - 7x + 6`

Answer

To factorise the expression \(2x^2 - 7x + 6\), we will use the method of splitting the middle term. Here are the steps to solve the problem:

### Step 1: Identify the coefficients
The given quadratic expression is \(2x^2 - 7x + 6\). Here, the coefficients are:
- \(a = 2\) (coefficient of \(x^2\))
- \(b = -7\) (coefficient of \(x\))
- \(c = 6\) (constant term)

### Step 2: Calculate the product \(ac\)
We need to find the product of \(a\) and \(c\):
\[ ac = 2 \times 6 = 12 \]

### Step 3: Find two numbers that multiply to \(ac\) and add to \(b\)
We need to find two numbers that multiply to \(12\) (the value of \(ac\)) and add to \(-7\) (the value of \(b\)). The numbers that satisfy these conditions are \(-3\) and \(-4\) because:
\[ -3 \times -4 = 12 \quad \text{and} \quad -3 + -4 = -7 \]

### Step 4: Split the middle term
Now we can rewrite the middle term \(-7x\) using \(-3x\) and \(-4x\):
\[ 2x^2 - 3x - 4x + 6 \]

### Step 5: Group the terms
Next, we will group the terms in pairs:
\[ (2x^2 - 3x) + (-4x + 6) \]

### Step 6: Factor out the common factors from each group
Now we factor out the common factors from each group:
\[ x(2x - 3) - 2(2x - 3) \]

### Step 7: Factor out the common binomial
Now we can see that \((2x - 3)\) is a common factor:
\[ (2x - 3)(x - 2) \]

### Final Result
Thus, the factorised form of the expression \(2x^2 - 7x + 6\) is:
\[ (2x - 3)(x - 2) \]

---