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

Options

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

Answer

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

### Step 1: Use the Factor Theorem
According to the Factor Theorem, if \( (x - 2) \) is a factor of the polynomial \( f(x) = x^2 + 3qx - 2q \), then \( f(2) = 0 \).

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

### Step 3: Simplify the expression
Calculating \( f(2) \):
\[ f(2) = 4 + 6q - 2q \]
Combine like terms:
\[ f(2) = 4 + 4q \]

### Step 4: Set the expression equal to zero
Since \( (x - 2) \) is a factor, we set \( f(2) = 0 \):
\[ 4 + 4q = 0 \]

### Step 5: Solve for \( q \)
Now, we solve for \( q \):
\[ 4q = -4 \]
\[ q = -1 \]

### Conclusion
The value of \( q \) is \( -1 \).

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