Let `|(x,2,x),(x^2,x,6),(x,x,6)|=a x^4+b x^3+c x^2+dx+edot` Then, the value of `5a+4b+3c+2d+e` is equal 0 (b) -16 (c) 16 (d) none of these

Explanation

To solve the determinant \( |(x, 2, x), (x^2, x, 6), (x, x, 6)| \) and express it in the form \( ax^4 + bx^3 + cx^2 + dx + e \), we will follow these steps:

### Step 1: Set up the determinant
We start with the determinant:
\[
D = \begin{vmatrix}
x & 2 & x \\
x^2 & x & 6 \\
...