`Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)|` is divisible by a.`a+b` b. `a+2b` c. `2a+3b` d. `a^2`

Options

A. `a+b `
B. `a+2b`
C. `2a+3b`
D. `a^(2)`

Explanation

To solve the determinant \( \Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)| \) and determine which of the given options it is divisible by, we can follow these steps:

### Step 1: Write the Determinant
We start with the determinant:
\[
\Delta = \begin{vmatrix}
a & a^2 & 0 \\
1 & 2a+b & a+b \\
...