If `(x+1)` is a factor of the polynomial `p(x)=2x^(2)+kx` , then k =

Answer

To find the value of \( k \) such that \( (x + 1) \) is a factor of the polynomial \( p(x) = 2x^2 + kx \), we can follow these steps:

### Step 1: Set up the equation
Since \( (x + 1) \) is a factor of \( p(x) \), it means that when we substitute \( x = -1 \) into the polynomial, the result should be zero. Therefore, we can write:
\[ p(-1) = 0 \]

### Step 2: Substitute \( x = -1 \) into \( p(x) \)
Now, we substitute \( -1 \) into the polynomial:
\[ p(-1) = 2(-1)^2 + k(-1) \]

### Step 3: Simplify the expression
Calculating \( p(-1) \):
\[ p(-1) = 2(1) - k = 2 - k \]

### Step 4: Set the equation to zero
Since we know \( p(-1) = 0 \), we set the equation:
\[ 2 - k = 0 \]

### Step 5: Solve for \( k \)
Now, we can solve for \( k \):
\[ k = 2 \]

### Final Answer
Thus, the value of \( k \) is:
\[ \boxed{2} \]

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