Determine the value of a for which the polynomial `2x^4-a x^3+4x^2+2x+1` is divisible by `2x+1dot`

Explanation

To determine the value of \( a \) for which the polynomial \( 2x^4 - ax^3 + 4x^2 + 2x + 1 \) is divisible by \( 2x + 1 \), we can follow these steps:

### Step 1: Identify the root of the factor
The polynomial \( 2x + 1 \) can be set to zero to find its root:
\[ 2x + 1 = 0 \implies x = -\frac{1}{2} \]

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