If `x^3+a x^2-b x+10` is divisible by `x^2-3x+2,` find the values of `a` and `b` .

Explanation

To solve the problem, we need to find the values of \( a \) and \( b \) such that the polynomial \( x^3 + ax^2 - bx + 10 \) is divisible by \( x^2 - 3x + 2 \).

### Step-by-Step Solution:

1. **Factor the Quadratic Polynomial**:
The polynomial \( x^2 - 3x + 2 \) can be factored. We can find its roots by solving:
\[
x^2 - 3x + 2 = 0
...