If `(x-2)` is a factor of `(x^(2)+3qx-2q)`, then the value of q is :

Options

A. `-2`
B. `-1`
C. 1
D. 2

Answer

To find the value of \( q \) such that \( (x-2) \) is a factor of \( (x^2 + 3qx - 2q) \), we can follow these steps:

### Step 1: Set up the equation
Since \( (x-2) \) is a factor, we can substitute \( x = 2 \) into the polynomial \( (x^2 + 3qx - 2q) \) and set it equal to zero.

### Step 2: Substitute \( x = 2 \)
Substituting \( x = 2 \) into the polynomial gives:
\[ (2^2 + 3q(2) - 2q) = 0 \]
This simplifies to:
\[ (4 + 6q - 2q) = 0 \]

### Step 3: Simplify the equation
Combine the terms involving \( q \):
\[ 4 + 4q = 0 \]

### Step 4: Solve for \( q \)
Now, isolate \( q \):
\[ 4q = -4 \]
\[ q = -1 \]

### Conclusion
Thus, the value of \( q \) is \( -1 \).

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