If (y-1) is a factor of `(y^2+3qy-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 \( (y - 1) \) is a factor of \( (y^2 + 3qy - 2q) \), we can use the Factor Theorem. According to the Factor Theorem, if \( (y - 1) \) is a factor of a polynomial \( f(y) \), then \( f(1) = 0 \).

### Step-by-step Solution:

1. **Define the polynomial**:
\[ f(y) = y^2 + 3qy - 2q \]

2. **Substitute \( y = 1 \)** into the polynomial:
\[ f(1) = (1)^2 + 3q(1) - 2q \]

3. **Simplify the expression**:
\[ f(1) = 1 + 3q - 2q \]
\[ f(1) = 1 + q \]

4. **Set the expression equal to zero** (since \( (y - 1) \) is a factor):
\[ 1 + q = 0 \]

5. **Solve for \( q \)**:
\[ q = -1 \]

### Final Answer:
The value of \( q \) is \( -1 \).