Question

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).

Answer 1

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)