यदि `p(x)=x^(3)-x^(2)+2` तथा `g(x)=x+1` तब `p(x)+g(x)` तथा `p(x)-g(x)` की घात ज्ञात कीजिए ।

Divide p(x)=x^3+3x^2+3x+1 by g(x)=x+2

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following : i] p(x) = x^(3) - 3x^(2) + 5x - 3, g(x) = x^(2) - 2 ii] p(x) = x^(4) - 3x^(2) + 4x + 5, g(x) = x^(2) + 1 - x iii] p (x) = x^(4) - 5 x + 6 g(x) = 2 - x^(2)

divide p(x)=x^3+3x^2+3x+1 by g(x)= x+2

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following: (i) p(x) = x^3 - 3x^2 + 5x - 3, g(x) = x^2 - 2 (ii) p(x) = x^4 - 3x^2 + 4x - 5, g(x) = x^2 + 1 - x (iii) p(x) = x^4 - 5x + 6, g(x) = 2 - x^2

If p(x)=x^(3)-5x^(2)+4x-3 andg(x)=x-2 show that p(x) is not a multiple of g(x).

Check whether g(x) is a factor of p(x) by dividing the first polynomial by the second polynomial: (i) p(x) = 4x^(3) + 8x + 8x^(2) +7, g(x) =2x^(2) -x+1 , (ii) p(x) =x^(4) - 5x -2, g(x) =2-x^(2) , (iii) p(x) = 13x^(3) -19x^(2) + 12x +14, g(x) =2-2x +x^(2)

If g(x)=x+1 and p(x)=2x^3+x^2-2x+1 then (p(x))/(g(x))=?

By remainder theorem , find the remainder when p(x) is divided by g(x) where , (i) p(x) =x^(3) -2x^2 -4x -1 ,g(x) =x+1 (ii) p(x) =4x^(3) -12x^(2) +14x -3,g(x) =2x-1 (iii) p(x) =x^(3) -3x^(2) +4x +50 ,g(x) =x-3

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.

Let p(x)=x^(3)-x+1andg(x)=2-3x , Check whether p(x) is a multiple of g (x) or not .