If (x - 2) is a factor of polynomial p(x) = `x^(3) + 2x^(2) - kx + 10`, then the value of k is:

Options

A. 10
B. 11
C. 12
D. 13

Answer

To find the value of \( k \) such that \( (x - 2) \) is a factor of the polynomial \( p(x) = x^3 + 2x^2 - kx + 10 \), we can use the Factor Theorem. According to the Factor Theorem, if \( (x - c) \) is a factor of a polynomial \( p(x) \), then \( p(c) = 0 \).

### Step-by-step Solution:

1. **Substitute \( x = 2 \) into the polynomial \( p(x) \)**:
\[ p(2) = 2^3 + 2(2^2) - k(2) + 10 \]

2. **Calculate \( p(2) \)**:
\[ p(2) = 8 + 2(4) - 2k + 10 \]
\[ p(2) = 8 + 8 - 2k + 10 \]
\[ p(2) = 26 - 2k \]

3. **Set \( p(2) \) equal to 0** (since \( (x - 2) \) is a factor):
\[ 26 - 2k = 0 \]

4. **Solve for \( k \)**:
\[ 2k = 26 \]
\[ k = \frac{26}{2} = 13 \]

### Conclusion:
The value of \( k \) is \( 13 \).