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

Options

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

Explanation

To find the value of \( k \) such that \( (x + 1) \) is a factor of the polynomial \( (2x^2 + kx) \), we can use the Factor Theorem. According to the Factor Theorem, if \( (x + 1) \) is a factor of the polynomial, then substituting \( x = -1 \) into the polynomial should yield zero.

### Step-by-step Solution:

1. **Set up the polynomial**: We have the polynomial \( P(x) = 2x^2 + kx \).

2. **Substitute \( x = -1 \)**: According to the Factor Theorem, we substitute \( x = -1 \) into the polynomial:
\[ P(-1) = 2(-1)^2 + k(-1) \]

3. **Calculate \( P(-1) \)**:
\[ P(-1) = 2(1) - k = 2 - k \]

4. **Set the polynomial equal to zero**: Since \( (x + 1) \) is a factor, we set \( P(-1) = 0 \):
\[ 2 - k = 0 \]

5. **Solve for \( k \)**:
\[ k = 2 \]

### Final Answer:
The value of \( k \) is \( 2 \).

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