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 find the value of \( a \) such 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**:
Since \( x + 2a \) is a factor of \( p(x) \), we can set \( g(x) = x + 2a \). If \( g(x) \) is a factor, then \( g(-2a) = 0 \).

2. **Set \( g(-2a) = 0 \)**:
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