Factorise: `2n^2 + 3n`

Options

A. `n(2n^2+3)`
B. `n^2(2n+3)`
C. `n(2n+3)`
D. `n(2n-3)`

Answer

To factorise the expression \(2n^2 + 3n\), we can follow these steps:

### Step 1: Identify the common factor
Look for the common factor in both terms of the expression \(2n^2\) and \(3n\).

**Common factor:** Both terms have \(n\) as a common factor.

### Step 2: Factor out the common factor
Now, we can factor out \(n\) from the expression:

\[ 2n^2 + 3n = n(2n + 3) \]

### Step 3: Write the final factorised form
The expression is now fully factorised. The final answer is:

\[ n(2n + 3) \]

### Summary of the factorisation:
The factorised form of \(2n^2 + 3n\) is \(n(2n + 3)\).

---