When `x^3-2x^2+a x-b` is divided by `x^2-2x-3,` the remainder is `x-6.` The values of `a and b` are respectively.
(a)`-2, -6`
(b) `2, -6`
(c)`-2, 6`
(d) `2 , 6`

Explanation

To solve the problem, we need to find the values of \( a \) and \( b \) such that when the polynomial \( x^3 - 2x^2 + ax - b \) is divided by \( x^2 - 2x - 3 \), the remainder is \( x - 6 \).

### Step 1: Understand the Division
According to the polynomial division theorem, we can express the polynomial \( f(x) \) as:
\[ f(x) = (x^2 - 2x - 3) \cdot q(x) + r(x) \]
where \( r(x) \) is the remainder. Here, \( r(x) = x - 6 \).
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