Without actual division, prove that `2x^(4)-5x^(3)+2x^(2)-x+2` is divisible by `x^(2)-3x+2`.

Explanation

To prove that the polynomial \(2x^{4} - 5x^{3} + 2x^{2} - x + 2\) is divisible by \(x^{2} - 3x + 2\) without actual division, we can use the factor theorem. The factor theorem states that a polynomial \(f(x)\) is divisible by \(x - c\) if and only if \(f(c) = 0\).

### Step-by-Step Solution:

1. **Factor the Divisor**:
We start by factoring the quadratic polynomial \(x^{2} - 3x + 2\).
\[
x^{2} - 3x + 2 = (x - 1)(x - 2)
...