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

Options

A. `-3`
B. `4`
C. `2`
D. `-2`

Explanation

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

### Step 1: Understand the Factor Condition
Since \( x + 1 \) is a factor of the polynomial, it implies that when we substitute \( x = -1 \) into the polynomial, the result should be zero.

### Step 2: Set Up the Polynomial
Let \( p(x) = 2x^2 + kx \).

### Step 3: Substitute \( x = -1 \)
We substitute \( x = -1 \) into the polynomial:
\[ p(-1) = 2(-1)^2 + k(-1) \]

### Step 4: Simplify the Expression
Calculating \( p(-1) \):
\[ p(-1) = 2(1) - k = 2 - k \]

### Step 5: Set the Polynomial Equal to Zero
Since \( x + 1 \) is a factor, we set \( p(-1) = 0 \):
\[ 2 - k = 0 \]

### Step 6: Solve for \( k \)
Now, we solve for \( k \):
\[ k = 2 \]

### Conclusion
Thus, the value of \( k \) is \( 2 \).

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