On dividing $x^3-3x^2+x+2$ by a polynomial $g(x)$, the quotient and remainder are $(x^2-x+1)$ and $(-2x+4)$ respectively. Then $g(x)$ is

Explanation

Dividend = Divisor $\times$ Quotient + Remainder Now $x^3 - 3x^2 + x + 2 = g(x) \times (x^2 - x + 1) + (-2x + 4)$ $g(x) \times (x^2 - x + 1) = x^3 - 3x^2 + x + 2 + 2x - 4$ $= x^3 - 3x^2 + 3x - 2$ $g(x) \times (x^2 - x + 1) = x^3 - 3x^2 + 3x - 2$ $g(x) = \frac{x^3 - 3x^2 + 3x - 2}{x^2 - x + 1}$ $g(x) = \frac{(x-2)(x^2-x+1)}{(x^2-x+1)}$ $\boxed{g(x)=(x-2)}$