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).

Let p(x) = x³ - 3x² + x + 2, q(x) = (x – 2) and r(x) = (–2x+4)

According to Polynomial Division Algorithm, we have

p(x) = g(x).q(x) + r(x)

⇒ x³ - 3x² + x + 2 =g(x).(x−2)−2x+4

⇒x³ - 3x² + x + 2 + 2x −4 =g(x).(x−2)

⇒x³ - 3x² + 3x + 2=g(x).(x−2)

So, Dividing x³ - 3x² + 3x + 2 by (x−2), we get

(x² - x + 1)

Therefore, we haveg(x) = (x² - x + 1)