Question

class 10th from maths ncert chapter 2.3 question no. 4

Answer 1

Since on dividing x 3−3 x 2+x+2 by a polynomial (x – 2) × g(x), the quotient and remainder were (x – 2) and (– 2 x + 4) respectively, therefore,  

             Therefore, Quotient × Divisor + Remainder = Dividend

         ⇒ (x−2)×g(x)+(−2 x+4)  =x 3−3 x 2 +x−2

        ⇒ (x – 2) × g(x) =x 3−3 x 2+x−2+2 x−4

        ⇒ g(x)=x 3−3 x 2+3 x−2 x−2                  ... (1)  

        Let us divide x 3−3 x 2+3 x−2 by x−2. We get

          Therefore, equation (1) gives g (x) =x2−x+1