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

Explanation

To prove that \(2x^4 - 5x^3 + 2x^2 - x + 2\) is divisible by \(x^2 - 3x + 2\) without actual division, we will follow these steps:

### Step 1: Identify the Polynomial and its Divisor
Let \(P(x) = 2x^4 - 5x^3 + 2x^2 - x + 2\) (the polynomial to be divided) and \(G(x) = x^2 - 3x + 2\) (the divisor).

### Step 2: Factor the Divisor
We need to factor \(G(x)\):
\[
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