Find the quotient and remainder in each of the following and verify the division algorithm :
(i) p(x)`=x^(3)-4x^(2)+2x-1` is divided by g(x)=x+2.
(ii) p(x)`=x^(4)+2x^(2)-x+1` is divided by g(x)`=x^(2)+1`.
(iii) p(x)`=2x^(4)-3x^(3)+x^(2)+5x-3` is divided by g(x)`=x^(2)+x-1`.
(iv) p(x)`=x^(4)-5x^(2)+6` is divided by g(x)=x+2.

Answer

N/a

Explanation

(i) quotient`x^(2)-6x+14`, remainder=-29
(ii) quotient `=x^(2)+1` , remainder=-x
(iii) quotient `=2x^(2)-5x+8`, remainder=5-8x
(iv) quotient`=x^(3)-2x^(2)-x+2`, remainder=2