Here in the given question,
Dividend = x3 - 3x2 + x + 2
Quotient = x - 2
Remainder = -2x + 4
Divisor = g(x)
We know that,
Dividend = Quotient × Divisor + Remainder
⇒ x3 - 3x2 + x + 2 = (x - 2) × g(x) + (-2x + 4)⇒ x3 - 3x2 + x + 2 - (-2x + 4) = (x - 2) × g(x)
⇒ x3 - 3x2 + 3x - 2 = (x - 2) × g(x)
⇒ g(x) = (x3 - 3x2 + 3x - 2)/(x - 2)
∴ g(x) = (x2 - x + 1)