If x+a is a factor of `2x^(2)+2ax+5x+10`, find the value of a.

Explanation

To find the value of \( a \) such that \( x + a \) is a factor of the polynomial \( 2x^2 + 2ax + 5x + 10 \), we can follow these steps:

### Step 1: Set up the equation
Since \( x + a \) is a factor, we can substitute \( x = -a \) into the polynomial, and the result should equal zero:
\[ 2(-a)^2 + 2a(-a) + 5(-a) + 10 = 0 \]

### Step 2: Simplify the equation
Now, we will simplify the left-hand side:
\[ 2(-a)^2 = 2a^2 \quad \text{(since } (-a)^2 = a^2\text{)} \]
\[ 2a(-a) = -2a^2 \]
\[ 5(-a) = -5a \]
Putting it all together, we have:
\[ 2a^2 - 2a^2 - 5a + 10 = 0 \]

### Step 3: Combine like terms
The \( 2a^2 \) and \( -2a^2 \) cancel each other out:
\[ -5a + 10 = 0 \]

### Step 4: Solve for \( a \)
Now, we can solve for \( a \):
\[ -5a + 10 = 0 \implies -5a = -10 \implies a = \frac{-10}{-5} = 2 \]

### Conclusion
Thus, the value of \( a \) is:
\[ \boxed{2} \]