If `x+2a ` is factor of ` x^(5)-4a^(2)x^(3)+2x+2a +3` , then find the value of a .

Explanation

To solve the problem, we need to determine the value of \( a \) given that \( x + 2a \) is a factor of the polynomial \( P(x) = x^5 - 4a^2 x^3 + 2x + 2a + 3 \).

### Step-by-Step Solution:

1. **Identify the Factor Condition**:
Since \( x + 2a \) is a factor of \( P(x) \), it means that when \( x = -2a \), the polynomial \( P(-2a) \) should equal zero.

2. **Substitute \( x = -2a \) into the Polynomial**:
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