[" (12) Div.P( "x)=6x^(5)-x^(4)+4x^(3)-5x^(2)-x-15],[" by "g(x)=2x^(2)-x+3]

(5x^(2)-4+6x^(3))-:(-2+3x)

Check whether g(x)=2x^(2)-x+3 is a factor of f(x)=6x^(5)-x^(4)+4x^(3)-5x^(2)-x-15 by applying the division algorithm.

Divide P(x)=2x^5-5x^4+7x^3+4x^2-10x+11 by g(x)=x^3+2

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.

The product of uncommon real roots of the p polynomials p(x)=x^(4)+2x^(3)-8x^(2)-6x+15 and q(x)=x^(3)+4x^(2)-x-10 is :

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)

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)

x ^ (3) + 5x ^ (2) -2x-24, x ^ (3) -4x ^ (2) + x + 6