On dividing $x^3 - 3x^2 + x + 2$ by a polynomial $g(x)$, the quotient and remainder were $x - 2$ and $-2x + 4$ respectively. Find $g(x)$.

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Step 1: $x^3 - 3x^2 + x + 2 = (x - 2) 	imes g(x) + (-2x + 4)$
Step 2: $\Rightarrow (x - 2) 	imes g(x) = x^3 - 3x^2 + 3x - 2$
Step 3: $\Rightarrow g(x) = \frac{x^3 - 3x^2 + 3x - 2}{x - 2} = \frac{(x - 2)(x^2 - x + 1)}{(x - 2)}$
Step 4: $= x^2 - x + 1$

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