If `3x^(2)-6x+a` is divisible by `x-2`, then the value of 'a' will be

Options

A. 6
B. 8
C. 0
D. `-2`

Answer

To find the value of 'a' such that the polynomial \(3x^2 - 6x + a\) is divisible by \(x - 2\), we can use the Remainder Theorem. According to this theorem, if a polynomial \(f(x)\) is divisible by \(x - c\), then \(f(c) = 0\).

### Step-by-step Solution:

1. **Identify the polynomial**:
The polynomial given is \(f(x) = 3x^2 - 6x + a\).

2. **Set up the condition for divisibility**:
Since we want \(f(x)\) to be divisible by \(x - 2\), we need to find \(f(2)\) and set it equal to 0:
\[ f(2) = 3(2)^2 - 6(2) + a \]

3. **Calculate \(f(2)\)**:
Substitute \(x = 2\) into the polynomial:
\[ f(2) = 3(4) - 6(2) + a \]
\[ = 12 - 12 + a \]
\[ = a \]

4. **Set the equation to zero**:
Since \(f(2) = 0\) for divisibility, we have:
\[ a = 0 \]

5. **Conclusion**:
The value of \(a\) that makes the polynomial \(3x^2 - 6x + a\) divisible by \(x - 2\) is:
\[ \boxed{0} \]