Step-by-step explanation:

Dividend = Divisor × Quotient + Remainder

(x3 - 3x2 + x + 2) = g (x) × (x - 2) + (- 2x + 4)

(x3 - 3x2 + x + 2) - (- 2x + 4) = g (x) × (x - 2)

(x3 - 3x2 + x + 2x + 2 - 4) = g (x) × (x - 2)

(x3 - 3x2 + 3x - 2) = g (x) × (x – 2)

g (x) = (x3 - 3x2 + 3x - 2) / (x – 2)

On dividing x³ - 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x - 2 and - 2x + 4, respectively. Find g (x)

Therefore, g (x) = x2 - x + 1