Factorise the following :
`2x^(2)-15x +7`

Answer

To factorise the expression \(2x^2 - 15x + 7\), we will use the method of middle term splitting. Here’s a step-by-step solution:

### Step 1: Identify the coefficients
The expression is in the form \(ax^2 + bx + c\), where:
- \(a = 2\)
- \(b = -15\)
- \(c = 7\)

### Step 2: Multiply \(a\) and \(c\)
We need to find two numbers that multiply to \(a \times c = 2 \times 7 = 14\) and add up to \(b = -15\).

### Step 3: Find the two numbers
The two numbers that multiply to \(14\) and add up to \(-15\) are \(-14\) and \(-1\).

### Step 4: Rewrite the middle term
We can rewrite the expression by splitting the middle term using the two numbers found:
\[ 2x^2 - 14x - x + 7 \]

### Step 5: Group the terms
Now, we group the terms:
\[ (2x^2 - 14x) + (-x + 7) \]

### Step 6: Factor out the common terms
From the first group \(2x^2 - 14x\), we can factor out \(2x\):
\[ 2x(x - 7) \]
From the second group \(-x + 7\), we can factor out \(-1\):
\[ -1(x - 7) \]

### Step 7: Combine the factored terms
Now we can combine the factored terms:
\[ 2x(x - 7) - 1(x - 7) \]
We can factor out \((x - 7)\):
\[ (x - 7)(2x - 1) \]

### Final Answer
Thus, the factorised form of \(2x^2 - 15x + 7\) is:
\[ (x - 7)(2x - 1) \]

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